We need to first ask ourselves what is Space? What is Time? Then we can begin to answer your question after we define what these two are and the relationship between them.
According to Geometrical Mathematics and based on Numerical Vector Space is nothing more then an empty construct and has no Dimensions until you give it a coordinate. We can define space in many different coordinate spaces each with different amount of dimensional vectors.
0 Dimensional Space: Any arbitrary point without location or position or location:
It has no size, it is the empty set or null. It is everywhere
or it is also infinite since there are an infinite amount of points.
1 Dimensional Space: Any scalar value or measurement. Distance, length, an amount, etc.
2 Dimensional Space: Defined by two intersecting vectors that are orthogonal or perpendicular.
This gives us a range of rotation or an angle between two vectors(no area),
gives us area as is defined in the fist and most simplest of shapes the triangle,
then every other polynomial that upon approximation to Nth mount of sides
as the accumulation of sides approach +infinity thus a circle.
3 Dimensional Space: Is the integration of 2D Space by adding another intersecting vector at
the origin in which will give us Volume.
4+ Dimensional Spaces: Is the continuation of integration by an additional vector space added
orthogonally or perpendicularly at a specified origin.
Here is some mathematical proofs: I will use the property of squares for the simplest demonstration in 2,3 & higher dimensions! We will assume that values of X are [x: x > 0]
0D Space - Simply 0 or NULL!
1D Space - Length - any value X to the first power: Function: f(x) = x^1
2D Space - Area: - any area defined by length * width: Function f(x) = x^2
3D Space - Volume: - any volume defined by length * width * height: Function f(x) = x^3
4D Space - Not Directly Defined - Integration of Volume: Function f(x) = x^4
ND Space where N approaches +Infinity: Function f(x) = x^N
With this representation we can see that the different dimensions of space are integrations of each other as you increase the amount of perpendicular vectors and as a result the function to define the area, volume, etc. has a direct relationship to the next higher order of a polynomial function.
According to physics time is the elapse of moments while observing a particle or object that has motion or moves in reference to another object based on a specific point of view.
No matter how you study or work within physics equations time is always considered a factor! By definition in mathematics a factor is a part of a product through multiplication. Due to this we can always factor out anything that is classified as a factor. Therefore time can be factored out of space!
Yes it is true that Time or Motion can not exists without Space, however they are independent entities of each other, meaning that you do not need time to have Space! Yet time instantly becomes a factor in the moment that you begin to measure! Think of it this way, when you pick a single arbitrary point in space without any coordinate space which is defined as 0D space and you begin to move away from that point to another arbitrary space, the act of moving does two things; first it now defines those points to have location or position and the separation of two points defines length or vector space and the energy and force applied to enable motion to exist defines time!
Space is infinite and empty it is only a construct! Time and Motion are one and the same so to speak! The only difference between Time and Motion is that Time is the effect of Motion! Once an object or particle begins to move you then have time as a result of that motion! They coherently exist together! You can not have one without the other, but you can always factor out motion or time from the construct of space.
I reiterate this for many throughout the mathematical and scientific community would argue against this! One of the reasons they will argue against this is because the powers that be, spend BILLIONS on printing the Text Books for Universities, Colleges and Public Schools! They do not want to be wrong! It may seem a little biased but it isn't! An example of this, is when I was in my second year of College I had a simple debate with my physics teacher on the basis that Time is not the 4th dimension of Space! I even presented my mathematical backing and showed proof that I was correct! I think the following semester she either retired or left for a different position at a different school. I will argue my understandings to even the most prestigious minds in their respective fields!
I still have not answered your question yet on if the universe has a different age between different observers! We will define time as the resulting effect of the act of motion! So then this would imply how long has the universe been moving? This is a hard question to answer, and I do not want to get into the debate on how old the universe is. That is a different topic! I used the above mathematics to distinguish the difference between Space and Time! This is important because Space Is Infinite in direction, size, and dimension! It is Empty and It is Full, It is Nowhere and It is Everywhere. Where Time is the resultant of an object that resides within the construct of space that moves throughout it. We do know that Einstein stated that Time is Relative and this becomes important!
We know that the faster an object moves or approaches the velocity of light the slower time appears to move, also the more mass along with its degree of density an object has affects time as well! Image this for a moment: Imagine a planet that is relatively the same size and mass of earth, but is very close to a black hole or a super black hole. Depending on the gravitational effect of that black holes gravity on the outlying planet, a person or observer who is standing on its surface for say 1 (Earth) hour could in essence end up being between 8 - 20 years worth of time on Earth itself!. If an observer was able to be positioned within the vortex of a black hole, I believe that Time would be suspended and Time would be infinite due to the nature of the higher dimensional spaces! Not that one could physically survive but in a hypothetical approach!
In my own opinion based off of mathematical proofs, research and conventional understanding of nature, I could answer and say YES! The universe can be perceived to be different ages from different observers at completely different locations with completely different environments. However, the true underlying age of the Universe or Cosmos is ENDLESS! I believe that it was always here and will always be here! I believe that there is No End To It and that yes an Infinite Universe can still expand! To prove this it would involve going a little deeper down the rabbit hole and would involve other topics that many would become offended by, however I will always stick to my beliefs!
Let us take an understanding of this concept first! When a person thinks of something even before they begin to speak it or write it down, the thought itself is the ability for us humans to "Create" and in the meaning of this, I am referring to the ability that within the moment we think of something or have a thought, we make that idea or concept manifest and it becomes a tangible object. It may not be a physical object that we can see or touch but sure enough we make it exist! I will refer to our thoughts alone as being Eternity Past. In the exact moment that we speak or write out that thought, I will refer to it as Eternity Present! Once we speak the word or utterance the energy that comes from within us (our voice) which emanates Sound continues forever! We do not hear that Sound for ever because its amplitude (Volume) continuously decreases as it approaches 0 but it never reaches 0 and it travels on its trajectory forever, however Sound waves can be interfered with by other waves. The outgoing sound I will call Eternity Future! Examine this expression of words! Eternity Past + Eternity Present + Eternity Future = FOR ALL TIMES SAKE!
As you can see to answer some of the most difficult questions, can not involve just one single aspect of human understanding, you have to consider and expect many other aspects as well, not just the sciences! Science is a tool and nothing more! It is very useful and it is an amazing approach to study and solve problems! I do not take anything away from the sciences because personally I enjoy them! However, like I said not every question can be answered by science alone! Keep this thought in mind!
I do not argue that the "Event - The Big Bang" had occurred: I will however argue that the Big Bang was not the beginning nor the initial event. I will argue that there was substance before the Big Bang!
This next part, I am using for reference for this coincides with my own beliefs! I will use only 3 versus and I will break them down part by part and I will use mathematical and scientific notations to back up and prove my synopsis!
1] IN the beginning God created the heaven and earth. 2] And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. 3] And God said, "Let there be light:" and there was light."
Before I break this down, this is not to be considered a method of pushing my own beliefs onto others, this is not what this is about! I personally believe this and I am using this and including this as a reference! I believe in Free Will and Choice, and I like to share what I know. Once I pass on the information at hand, I leave it at that, and it is up to the other person (observer) to do what they will with it or to make up their own mind!
We see here that the time frame and place is the beginning. We see that He created the heaven and earth. Let's pause here for a moment. In the Hebrew language the word used for our word heaven is always used in the plural! Let's not think of this as being the Spiritual Heaven as in Heaven or Hell. Think of heavens being Space as I described above having an infinite amount of dimensions no size, being everywhere, think of it as being a construct! The word earth, this is not to be confused with our planet called Earth, think of this on the lines of substance, matter, etc.! The creation of the Spaces 0D, 1D, 2D ... ND was created and the substances within it (I will come back to this a little later). What were the conditions at this point? It was without form, it was void, and darkness was upon the face of the deep. Okay that is simple, there is no shape for it is null and void, darkness is everywhere and the phrase upon the face of the deep refers to everywhere and in all directions and dimensions. Remember at this point there is no shape nor size, and it is completely pitch black across all Eternity. Then the Spirit of God moved amongst or across the waters! We need to understand that everything we do within the physical is only a sub part of the Spirit! Spirit is Eternal and can not be defined by scientific models! It can however be described by mathematical notations such as Infinity which means the same as Forever or Eternity and we know that these concepts do exist! This was only mentioned to clarify a few things. What is important at this point is the word waters meaning more than one! How many? There is no count for it is just plural; implying an infinite amount of waters. We need to stop here for a moment and consider the importance of this word waters!
The word waters that is used is very significant and very important! Why and how? Do not think of this as in being water on Earth for that will mislead you! Ask yourself what is the most abundant element in all of the Cosmos? What element are all of the stars mostly made of? The answer is definitive and simple! It is the very first element on the periodical table and that is Hydrogen! Hydrogen is unique compared to all other elements that precede it in that abundantly and mostly commonly found in all of nature it has 1 Electron and 1 Proton and 0 Neutrons! There are isotopes that do exist in nature but they are scarce and rare, but they are infinite as well. What does Hydrogen have to do with the term waters? Everything! On Earth Hydrogen exists naturally as a gas, but if you put it in darkness removing any light from it, it will lose heat and its temperature will drop and it will go from a gas to a liquid, hence water, and since there are an infinite amount of hydrogen atoms there is the implied word waters!
Now remember at this point of time it is dark everywhere, this means there is no heat from light and everything is atomically frozen! Essentially every Hydrogen Atom is completely frozen at 0 Degrees Kelvin. The construct of space is there with an infinite amount of dimensions and expands out forever, it is no where it is everywhere, and it is full of an infinite amount of these frozen Hydrogen Atoms, only protons and electrons exist at this point. There are no neutrons or photons yet, the Cosmos are Infinite and it is static! After the Spirit of God flowed through this construct that he just got done creating he then Spoke! What were the Words of His Voice? "Let there be light"
The first word is Let, this can also be referred to: to allow, bring forth, etc. The word there: Here, There, Every Where!. The word be: to exist, to be manifested. The word light! Well lets just say it is light!.
In the exact moment of this phrase for the first few words just before the word light came out, think of this infinite construct of absolutely frozen hydrogen ice begins to resonate or vibrate. At this point in time from the words "Let there be," caused all of the static electrons and protons to begin to vibrate, but they are all in unison so this construct now has potential energy. It is now filled with Sound which is a form of energy! Then the word light came out, and now this word because of its meaning, and being that it is at this instance being manifested into existence now comes forth and at every single possible location shines forth and separates this construct into multiple constructs. This is what I refer to as the Big Bang! In the moment that Light was Spoken into existence is the same exact moment that the Big Bang had occurred. However, there was not just one Big Bang, there were an Infinite amount of Big Bangs! This is easy to believe too! Just look at any single Galaxy that has a Super Black Hole at its core! These black Holes are where the initial Light came forth! There are an infinite amount of Galaxies! And yes the galaxies are expanding away from each other!. There are two distinctive forms of energies that exist! Sound and Light! All others are combinations of the two! In this moment when light came to be, we have to understand that Sound came first then Light, but both happened simultaneously and Light traveled past the initial Sound! It may seem to be contradicting but it isn't! Think of this: as an observer during a storm, we see the lightning first then hear the thunder, but what if I was to tell you that the lightning is the result of the thunder, yet you perceived the lightening before the thunder?
This can be proven mathematically too! Think of this: sound moves in waves such as the two trig functions sine and cosine which are properties of triangles and the rotation of angles. Think of light moving in a linear fashion: This gives rise to linear equations and every other polynomial algebraic function. When you look at the generic graphs for:
f(x) = sin(theta), f(x) = cos(theta) they are continuous functions oscillatory functions, meaning sinusoidal: Properties of Sound Waves. When you look at the generic functions of f(x) = mx + b, f(x) = ax^2 + bx + c, f(x) = ax^3 + bx^2 + cx + d, and so on for every polynomial function other then root linear function all others will have similar properties based on their highest order of exponent value giving us (Even) & (Odd) functions. All even functions are similar in nature, and all Odd Functions are Similar in nature. These series of functions can be used to represent Light depending on which Dimension of Space you are working in!
It was not until the moment that Light was spoken into existence that Time Began to Exist. It was at this point of time that everything began to move, began to have shape and form, and was no longer void or dark. There is no such thing as Empty Space in this sense because it is filled with substance! Yet Space itself is empty! Space is just the construct! Matter is Only the Substance! The two infinite energy sources that gives everything its properties, Sound and Light are what gives you Motion And Time! No matter where you look, everything is in Motion!
This can be proven even more. One person once said, "Matter nor energy can not be created nor destroyed it can only be transferred or transformed", along with the relationship of energy and matter <--> E=mC^2.
Do to relativity in one observers perspective, frame of reference, point of view, and their own personal belief can be completely different from another's! I hope this helps you in your quest for a Higher Understanding of Things! I know this is very long, but sometimes the easiest of questions to ask are the hardest to answer, and they can also present even more questions to be asked and lead to more answers to be desired! How far down the rabbit hole do you truly want to go?