Dr. Craig is a liar.

[LostLocke]

There's a problem right there. We don't actually know that the universe "began" to exist.

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.