As I understand it,the evidence is clear that the universe was in a very hot dense 13.7 billion years. If you assume GR can describe the universe at the smallest scales then time may stop around this time.
NOW THE CAVEATS:
We have to assume GR is good to these tiny scales. Gr has never been tested down to these tiny scales and so one might argue there is no good evidence for the conclusion of no time before the big bang.
Other quanutm gravity models for example, Loop quanutm cosmology predict there was time before the big bang. see for example
http://arxiv.org/abs/0812.4703
Another assumption one has to make is inflation is not eternal, accoprding to Guth most models of inflation imply its eternal, which implies our big bang is only one of many and there's no reason to think ours is the first. See:
http://arxiv.org/abs/hep-th/0702178
Its also possible to construct models that have no inflation and no quantum gravity corrections that still imply our big bang is one of many eg Penropse CCC:
http://en.wikipedia.org/wiki/Conformal_Cyclic_Cosmology
There are many other models too frequent to mention to be honest.
Bottom line: the idea that time began at the big bang is one conjecture out of many, at the moment we don't know if it or alternate models such as quanutm bounce, CCC, eternal inflation, ekprotic etc are correct. So we should keep an open mind.