Can Time Exist Before the Big Bang?

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If we calculate Birth of Time then T= 0 or T ≠ 0.
If Big Bang cause time then should we consider Big Bang time T = 0.
But in real life we do have numbers beyond 0. Example : -1 , -2, -3 ...-1000 & so on.
We represent space-time with numbers which are infinite on both side before 0 & after 0...
so how space-time can be finite starting from Big Bang ?
Can we consider Space-time was traveling in high dimension before Big Bang.
 
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If Big Bang cause time then should we consider Big Bang time T = 0.

The Big Bang was a process, not an "event". It describes the early expansion of the Universe, not its beginning.

We represent space-time with numbers which are infinite on both side before 0 & after 0...
so how space-time can be finite starting from Big Bang ?

The same way that I can have a finite collection of objects, even though the set of natural numbers is infinite. Mind you, the infinitude of space is not an entirely settled issue.

Can we consider Space-time was traveling in high dimension before Big Bang.

I have no idea what this means.
 
Time is a measure of change. In cosmology change is usually expressed in terms of a scale factor - a(t) - where t is the time elapsed after the big bang. It is a simple idea, the universe gets bigger as t increases, and smaller as t decreases. Can t be negative? We don't know. Mathematically, it is certainly possible, and it is widely believed the universe is mathematically consistent. It is, however, unclear if any actual physical meaning can be attached to values of t < 0, or even to t = 0. For that reason cosmologists say the big bang theory does not describe the universe at t = 0 and often say the very concept of time before the big bang is meaningless.