Dr. Craig is a liar.

[Jehanne]

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.

You're simply trying to explain one unknown ("the origin of the Cosmos") with an even bigger unknown ("god").  Instead of saving that god is a necessary being who has always existed, why not say that Nature has a foundational existence which is "necessary" and therefore uncaused.  Why not say that abstract objects, which are eternal, created the Cosmos?