Dr. Craig is a liar.

[SteveII]

You are right, we do not "know". But the point is that it seems it did under most theories developed from our knowledge of physics. >50%

Not really. We can trace it back to the beginning of its current state, but that still gives us no idea if it really "began'.
Just a heads up, the singularity and the 'big bang' are not the "beginning to exist" of the universe.

And what is the singularity? My understanding is that it is a mathematical idealization and not a physical entity. It is a boundary point. Metaphysically equivalent to nothing.