Could it Be That Our Universe Never Had a Beginning?

Here is an interesting scenario I have wondered myself, so I'd appreciate any input on it since I'm not a scientist:

Brian Flatt asked it:

Or maybe...time is like in calculus where, when you go backwards in time towards the big bang, you can approach but never actually reach the big bang itself. Scientists say that their science only works back to some infinitesimally small fraction of a second after the big bang, before that the science breaks down. So maybe, if you can approach but never reach the singularity itself, time HAS always existed, therefore space and the universe HAS always existed, which means there WAS no beginning, a beginning being only an illusion.

This question is tucked away in this post of his.

What d'ya think?