How can we say time began at big bang? I have seen many times scientists refer to time when Big Bang took place and space and time born out of singularity.
'Beginning of Time' is a very misleading statement,because process of beginning would consume some finite time which in turn mean that time was already present. So did the time really born out of some process ?
*I am not a physics person. But certainly would have become if I did not chose Software's :) , So forgive me if I missed something here.

-- Updated question
Let me rephrase my question
There is no doubt that in 4d model of space and time we cannot go deeper than center of universe(which is practically before the beginning of time).
1.Is universe is expanding at all? If yes then is the time also expanding along with space? 
Maybe we cannot ask above question about the expansion because we need reference of time to prove that universe(space and time) is expanding which we do not have in 4d model. But Big Bang surely talks about expansion of space (not sure about time). What does it mean when we say space (and time?) is expanding? 
Once we say that there is static 4d model of universe containing time as a integral part of space, Can we ask question about beginning of this 4d model? If not then the most troubling question is what is this all? and why it existed?,;) I do not expect the answer to this question, as I know we are still struggling to find best answers for them ;),
 A: Physics makes a model of spacetime. Every point in a 4d manifold corresponds to a time and a plane together.
For instance you could choose the 4d to be $$\{(a,b,c,d):a,b,c,d\in \mathbb R\}.$$
And then you could let time be $t=\sqrt{a^2+b^2+c^2+d^2}$ and all you need know is to specific the metric at each point. The metric tells rulers where to leave marks and clocks when to tick.
An easier to visualize example is $$\{(a,b,c):a,b,c\in \mathbb R\}.$$
And then you could let time be $t=\sqrt{a^2+b^2+c^2}$ in this example. And in this example you see time is the distance from the origin. And for each time you get a spherical shell. By adjusting the metric you can make the shell be whatever size you need at that time.
Now when you ask about before the big bang it's like asking what is deeper than the center of the earth. It's not even a question. And when you ask what the universe expands into, it expands into the future.
You can do the same with all our observations so far. They fit with having a really big spherical shell (in 4d, so it's a 3d shell) at our time and a smaller shell at earlier times. And the big bang is the center. And there isn't a before. No one every claimed there was a before. And there are models without one, so really it's just an assumption when someone assumes there is one.

I would like argue with a point you have made about nothing exist before big bang.

Would you also like to argue with me if you claimed that there is something deeper than the center of the earth. Because I said time is measured by the distance from the origin in 4d. So before time zero is just like being deeper than the center of the Earth.

If there was nothing big bang wouldn't have instantiated to form the universe. 

I don't know what you are saying. There isn't some point deeper than the center of the earth from which the earth springs. I even made a 3d version just to be easier to visualize. There is now, which is like the surface of the earth. Then there is yesterday which is like the surface one meter below the surface. Then there is last year which is like the surface one kilometer below the earth. And there is a billion years ago which is a small surface halfway towards to the center of the earth. And the big bang is the center of the earth. Insisting that there is something deeper than the center just shows that didn't pay attention to the words surface or deeper.
Spacetime is a unified 4d object, it isn't a series of spaces at different times.

Once you say that universe has instantiated you inherently assume presence of time in some form before universe began. 

First, I didn't say instantiate. That's you putting words into my mouth that I didn't say. Second that's simply not true. Pretending people said things  they didn't say and then claiming it means something it doesn't mean is pretty pointless. All of your comments simply show, in every way possible, that you didn't read my answer.
Time isn't a thing. Space isn't a thing. spacetime is a thing. Spacetime is a unified 4d object. And time could simply be a 4d distance from the 4d origin. Of that is hard to visualize try a 3d spacetime, make time be the 3d distance from the 3d origin and then at each time there is a 2d space and it is bigger for each time. There isn't any instantiation. And there isn't anything before time zero because in this model time is simply the distance from the origin.

I know it's a kind of logical deadlock

There is no deadlock. You claimed I said thing I didn't say. You clearly didn't read my answer. In fact, bringing up new words like instantiate just shows that you have baggage. Rather than learning to extract predictions from a model (i.e. to do science) you want add your baggage on top. People tried that for thousands of years, and it's not a deadlock, it's actually just tactic that doesn't make progress.
To do science you have to learn to make models and how to extract predictions from the models. Science isn't about looking at a model and ignoring it's predictions and instead making up words based on your baggage and then trying to insert your words into the model.
The model has its own terms such as 4d objects and their 4d point. And when we make a model we have to use the model's objects and terms to extract predictions. Then we compare those predictions to observations. And we judge the model based on how the predictions match the observations.
Sure, in the dark ages or the stone age the model might be judge for reasons besides how the prediction matches the observations. But that's why they didn't make progress.
There isn't a deadlock. You just aren't doing science. In science you judge models based on whether their predictions match observations. And to do that all you need is to understand the terms in the model and how to get predictions out of the model. You never need to bring up anything else. Well, if you have a class of models that you are unsure about you might want some statistics to discuss the probability that some of the many models mat H your actual observations. But for each model all you need to care about is the predictions.

but we have to solve it if we really want to understand space and time. 

To solve what? Are you going to solve the question of what's deeper than the center of the earth? It's just as meaningful. And since its not meaningful it's just as important (not all important).

I believe if human mind can think and ask questions about before big bang, something has to be there before the big bang, 

If the human mind can think and ask questions about deeper than the center of the earth, there must be something deeper than the center of the earth?
Besides, I dispute your claim that you asked a single question about "before the big bang" because I presented a model where that question didn't make sense and you just asserted it anyway. So it's just words. It's not a model, it's not an understanding, it's not even a scientific question. Scientific questions are about things that can be observed.
Sure there are models without a big bang. And they might have a period of time that was very hot and dense and those models might have times a trillion years ago. But hose are just different models, ones without an actual big bang. So they don't have a before.
A: I am not entirely certain of what you are asking, but I will try to answer what I do understand. The Big Bang is referred to as the 'Beginning of Time' simply because it is the event that theoretically kickstarted the universe. There is no scientific evidence for an event taking place before The Big Bang, so it is the beginning of the universe's timeline. Because the Big Bang is the first event in our history of the universe, there is no need to extend time to before the Big Bang because, to the best of our knowledge, there is no event to document before the Big Bang. Time realistically would have no beginning or end because for even the farthest point in time we can possibly imagine, we can always ask what happened before then, thus time having existed before that time. What I am saying is that we cannot put a cap on time, there just comes a point that documenting time becomes necessary no longer. I hope this could be of some help answering your question.
