That depends on how you define time, as well as whether it is linear or not. If not, then so far we cannot currently tell. Every yes answer will have a no, and vice versa. I also wouldn't be saying time started at any given point if I was a physics teacher.

Even if it were possible to build a time machine, the very atoms it was made of would be crushed before it reached the big bang. Nevertheless, mathematics can go back much further.

From what I understand of these things, as you approach the moment of the big bang space tends towards a state of infinite compression, but as it does so, time equally tends towards a state of infinite dilation. Consequently, you could never quite reach the big bang, let alone go beyond it, just as you can never quite reach the speed of light. Hence any discussion of "before" the big bang, or any idea of a "cause" for it is probably meaningless.

That said, as you approach a size for the universe of the order of the Planck Length (at an age of around a 10 million trillion trillion trillionth of a second, if I can count my zeros), all bets are off, since time and space become meaningless and all the known laws of physics collectively break down.

Rather than asking about "before" the big bang, a still more interesting question (and just possibly a more meaningful one) is why do we have a universe at all, instead of nothing, not even space or time? I didn't ask for one. Did you? Hands up anyone?

From the point of view of any possible observer, there was no time before the Big Bang. Time and Space are deeply interconnected - hence the term spacetime - and as there was no space before the Big Bang there could likewise be no time.

However, I must emphasise that this is true only from the point of view of an observer within the universe. If some external observer were to witness the birth of our Universe, then for that observer there must be a location from which to observe, and therefore a time to exist in.

From a theoretical point of view it is possible, using a multidimensional view of the universe(s) as in string theory, to calculate beyond the Big Bang, though the best bet for reaching back this far may be the elusive 'Theory of Everything', once gravity has been included in the forces that physics can unify into a single and coherent theory of the Universe.