Did spacetime start with the Big bang? Did spacetime start with the Big Bang?  I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before the big bang?
 A: I'm not a cosmologist either, which at least means I can speak in simple terms that don't assume you are deeply familiar with every mathematical permutation of the subject.
As I understand it, the universe is expanding, not just in the sense of the material in it spreading out, but in the sense that space-time itself is expanding. If we run the clock backwards, then, everything comes together at a point, including space and time. Of course, physicists can't really model the point itself, but they can model the properties of the universe as we get close to the point and amazingly, the predictions seem to generally agree with what we see. Hence the idea of the Big Bang.
But the human mind evolved in space time, so inevitably people picture this as a void in which there's nothing for awhile and then the universe explodes into being. This has to be wrong, though. What exactly is the void in this picture, since space does not yet exist? How can there be "awhile" before the big bang if time didn't exist "yet"? (Here the grammatical structure of our language works against us, since it assumes we are talking about something happening in space-time.) The simple way to keep your thought pictures honest is to remember that we can't see the universe FROM THE OUTSIDE, so don't try to picture it this way. The Big Bang can only be honestly pictured from inside the universe, so there's no meaning to the question of what happened "before" the Big Bang - it's a non sequitur. Similarly with the question "What was there before the Big Bang?" There "was" (time) no "there" (space) for there to be anything in. 
It sounds like you've already thought of this, which I take it is why you're asking the question. I don't think it is unreasonable to suspect that the earliest moments of the universe are not well modeled by the mathematics of infinities and infinitesimals, and that we don't really have a good grasp on this yet despite the agreement with the empirical data we have so far.
But don't get sidetracked by physicists who get so caught up in the math that they forget that the model is not the thing modeled.
A: The only well tested theory of gravity we have right now is general relativity (GR). In models based on GR, time and space only exist for $t>0$. 
This raises the question of what caused the big bang. In relativity, we use the term "event" to mean a certain position in space at a certain time. The big bang is not an event, because there is no time $t=0$. If you want to find a cause for some event happening at a given time $t>0$, there is always some earlier $t'$, with $0<t'<t$, that can supply that cause. So in this sense, the big bang doesn't require a cause, because only events require causes, and GR doesn't describe the big bang as an event.
We also have fundamental reasons to believe that GR is inaccurate under the very dense and hot conditions at $t < ~ 10^{-43}$ s (known as the Planck time), because of quantum-mechanical effects. If we had a theory of quantum gravity that worked under those conditions, then it might turn out that the singularity at $t=0$ was not real, and events at $t>0$ could be explained in terms of causes at $t<0$. This is what seems to happen, for example, in loop quantum cosmology. However, nobody has a theory of quantum gravity that  works and has been tested against experiment, so we don't really know.
A: Bear in mind that the real solution for the de Sitter spacetime is a scale factor
$$
a(t)~=~\sqrt{\frac{3}{\Lambda}}\cosh \left(t\sqrt{\frac{\Lambda}{3}} \right)
$$
for $\Lambda$ the cosmological constant.  $\Lambda$ was very large in the early universe, and it is not unreasonable to think that the universe was connected by the “throat” to the other half of the hyperboloid.
This is similar to the problem of the white hole, which is the other half of the Schwarzschild metric.  We generally ignore that, and so too most often the de Sitter spacetime is physically considered to be an exponentially expanding space where $\cosh(x)~\simeq~\exp(x)$ for large $x$.  So we start with the FLRW energy equation
$$
\left( \frac{\dot a}{a} \right)^2 = \frac{8\pi G \rho}{ 3} \; – \; \frac{k}{a^2}
 $$
Here "dot" means time derivative.  This equation can be derived using Newton's laws, or the energy of a projectile moving in a gravity field.
The other half of the hyperboloid might physically involve an instanton state, or tunneling state. The Schrodinger equation for a particle moving in one dimension with some potential $V$ is
$$
i\hbar\frac{\partial\phi}{\partial t}~=~-\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}~-~V(x)\psi
$$
If we consider a stationary case with a phase $\psi(x,t)~=~\psi(x) \exp(-iEt/\hbar)$ the left had term just becomes $E\psi$, where $E$ is the energy of the particle.  Now let us rearrange things so that 
$$
\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}~=~(E~-~V(x))\psi
$$
For a particle moving in space we set $\psi(x) \; \sim \; \exp(ikx)$, do the two derivatives and cancel out the ψ(x).
$$
k^2 \;= \; \frac{2m}{\hbar^2}(E \; – \; V)
$$
The funny thing is that for $V~>~E$ we have an imaginary $k$.  This means that the kinetic energy is in a funny sense negative, which is not something you expect in classical mechanics.  For a system of this sort it is in a classically forbidden region, and in more general systems there may be some dispersion $\omega~=~\omega(k)~=~vk~+~\dots$, which leads to an imaginary frequency.  The phase for the system is $\exp(i \phi) \; = \; \exp(i \omega t)$.  The imaginary quantity associated with the angular frequency ω may be reassigned to the time $t$, that is a mathematical triviality.  So in some of these problems it is useful to use this and work with imaginary time, or what is sometimes called Euclideanized time.
So the other half of the hyperboloid might be physically modeled to be a tunneling of a cosmology across a potential boundary.  This might then be an instanton due to a “blob” of vacuum energy which quantum escapes from another spacetime.  So from that setting if may be seen that the universe has some sort of precursor. or is quantum mechanically tied to another spacetime.  This might then be seen in the setting of a multi-cosmological universe or within what is called the multiverse.
A: The main theory which describes Space-Time and from which the prediction of the Big Bang comes is called General Relativity, from Einstein. This theory has several mathematical solutions and cosmologists worked to determine the most accurate. There are a class of alternatives but they all have the property that the equations which describe this solution have a singularity at $T=0$. Furthermore when this situation is examined physically it seems that there is a high density of all the Universe's matter there and then. So it is called the Big Bang.
The Singularity means that some terms become infinite and others unhelpfully become zero. So General Relativity has not been able to predict (or retrodict) what happens before, or how this process really began. The general assumption has been that it was some kind of giant Quantum Event. This assumption, when explained using a more complete theory of Quantum Gravity, may yet be correct.
However in the last few years, several mathematical cosmologists have taken seriously the idea that there was a Pre-Big Bang. Part of the reason for this may be because of the Cosmic Background Radiation data from satellites like WMAP. This data shows larger scale structure in the early universe than the older theories would have predicted.
In particular Roger Penrose has developed a view that the period since the Big Bang should be called an aeon, and that there were earlier aeons each infinitely long. This makes the Big Bang a kind of transition period between two aeons. The theory is speculative in several respects, but it is based on some mathematical constructions in General Relativity. This theory is called Conformal Cyclic Cosmology (CCC for short).
A recent short paper Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity gives the general idea. Although it is technical in places it demonstrates the kind of evidence that is motivating this theory. There are references in that paper to a book and other papers which describe that theory.
There are other theories around too, which suggest a pre-Big Bang model, perhaps other answers will mention those.
A: There are several cosmological models that are eternal to the past, as well as to the future: They include Aguirre & Gratton's 2003 "Steady-state eternal inflation" (vetted as plausible by Borde, Guth, & Vilenkin, in the last footnote to the last [2003's] version of the BGV Theorem, which is often misinterpreted as completely prohibiting past eternality, but actually only prohibits past eternality in models which are not "on average expanding"), Nikodem Poplawski's 2010 "Cosmology with torsion", and the 2010 "Conformal cyclic cosmology" formulated by Roger Penrose, who was awarded a 2020 Nobel Prize in Physics for his work on black holes, that are a major factor in that model.
The model by Aguirre & Gratton consists of two inflationary universes, each expanding at a quasi-exponential rate, that are causally-separated by a Cauchy surface: The "arrow of time" in each of them points in the temporal direction opposite the other's.
In Poplawski's torsion-based model, any large rotating star whose nuclear fuel has been depleted collapses gravitationally under its own weight due to the lack of radiation pressure adequate to prevent such a collapse, with the event horizon of that collapse combining with tidal effects to materialize fermions by separating them from their partners in particle-antiparticle pairs. The newly-materialized fermions interact with the stellar fermions (that are initially much larger), and that interaction spins the newly-materialized ones outward to form a new "local universe" that expands outward, at first at a quasi-exponential inflationary rate (although none of the specialized "inflaton" particles, found in older models of inflation and still only hypothetical, are required). Poplawski analogizes the shape of the new LU to "the skin of a basketball". Expanding indefinitely after its inflationary phase, it eventually contains black holes of its own, which repeat the process, apparently on sequentially-decreasing scales.
Although Penrose's 2010 model did suffer from the unclear and rather dubious evidence mentioned in the comments on an earlier answer to the OP's question, other evidence (found more recently) has supported it, as described in the 2020 revision of a paper by Meissner, An, and others, which described "spots of significantly raised temperature" that can still be observed in the Cosmic Microwave Background: Penrose considers those spots to represent the Hawking radiation of black holes from earlier "aeons" (in other words, earlier temporal iterations of a single universe much like our own). That paper appeared several months before Penrose's receipt of a 2020 Nobel Prize in Physics, which, however, was attributed more generally to his work on black holes and singularity theorems. "Conformal" theory preserves angles but not lengths, and Penrose's "Conformal cyclic cosmology" considers the thermal equilibrium of each temporal iteration, in an endless series of them, as the "Big Bang" of the next, with the "conformal rescaling" (which might perhaps be compared to the changes in scale implied by Poplawski's model) permitting this possibility through a gravitational "clumping" of matter into black holes, accompanied and/or followed by the evaporation of all of it into radiation, during a period of time whose phenomenally long duration cannot be specified, owing to the eventual lack of the fermionic components which Penrose feels to be essential in any form of clock (natural or artificial).
Of these three models, all but Poplawski's rely on 1915's General Relativity: Poplawski's, instead, relies on 1929's Einstein-Cartan Theory, a version of relativity that was formulated (through collaboration between Einstein and Cartan) a few years after the discovery of particulate spin, and requires that fermions (i.e., "matter particles") have a tiny spatial extent, some few orders of magnitude greater than the Planck length (which is the shortest distance observable through the magnification energies and procedures that are currently available to us). However, as each of his "local universes" inherits its direction of rotation from its "parent", his model would be falsified if astronomical evidence failed to reveal a prevalent direction of motion. Such a prevalence appears to have been discovered recently, by the astronomer Lior Shamir.
Aside from that last bit of observational evidence, I have to add a preference for Poplawski's model over the other two I've mentioned as having the same characteristic of eternality both to the past and to the future.  My preference is partly because it doesn't (unlike Penrose's) require a singularity, and partly because the formation of the sequential "local universes" more-or-less concentrically within each other, in the Polish-American physicist's model, might provide a gravitational reason for that expanded distribution of matter which accompanies the expansion of space that was fairly well-established by the SN1a experiments of the 1990's. (The 2021 version of a preprint by Poplawski, freely visible at https://arxiv.org/abs/1906.03947, eliminates both fluids and subatomic particles as possible forms of dark matter.)  By integrating scalar changes between large and small into the passage of time, each of the LU's in Poplawski's model would also provide the clearest example of a universe "expanding into itself", to use the terminology cited in the remark (mentioned earlier in this Q&A) by Nobel laureate John Mather.
As each local universe in Poplawski's cosmos continues expanding "indefinitely" after the bounce I've described (or a series of them, linked to baryogenesis with the temporal spacing that Gamow had first related to the proportions of various elements found within each LU), the overall effect is that averaging between expansion and contraction which was required by BGV.
Since it had been discouraged by a traditional assumption that infinity might necessarily lack any inherent shape, the plausibility of closed local universes or bubble universes, in Poplawski's and other models of an inflationary multiverse, has been greatly increased through a recent study of CMB data by Joseph Silk and collaborators, published in Nature Astronomy, Vol.4, Feb. 2020, p.196-203.  (The magazine article, titled "Planck evidence for a closed Universe and a possible crisis for cosmology", is currently available free online, but that may change.)
A: This relies on an empirical finding as to whether spacetime is finite or infinite. We already know that the Big Bang occured a finite amount of time ago.
If spacetime now is discovered to be finite then the Big Bang started at a point.
If spacetime now is discovered to infinite then spacetime at the Big Bang was also infinite because infinity divided by any finite number is infinite. It also means that the Big Bang didn't occur at a point but everywhere, all at once, in an immense flood of light. I say light, because everything at the Big Bang was massless (the Higgs field, at the Big Bang has a vev that is too low to give any elementary particle, including the Higgs boson, mass) and hence moved at the speed of light and so was akin to light.
It also shows that the density of particles at the Big Bang can't have been infinite either, again because infinity divided by any finite number is still infinite).
Hence, let there be light as a description of the world is pretty accurate.
A: I seriously doubt that.
There are quite a few theories trying to discuss "the beginning of the universe", and not all of them agree with having a "beginning" to the universe.
I don't have concrete facts to support what I'm about to say so consider it as "just another idea."
"Our whole universe was in a hot dense place, then fourteen billion years ago expansion started."
So there was a big explosion, and everything tried to get away from every other thing. This process has been going on for about fourteen billion years, and it will eventually stop. Because a big portion of the attracting/repelling forces (electromagnetic force which can attract and repel) will have been neutralized (like a stone which does have electrons and protons but doesn't attract or repel), and the attracting forces (gravity) will take over. The universe starts to get smaller and denser, and collapse into a small hot dense place, and in "hot places", the repelling forces will eventually take over, and so another bang happens, and it will create a universe much like of our own.
