Oh yeah. This is a big one. It is used by virtually every disciple of evidentialist apologists (and is attacked in basically every atheist book that discusses the issue of God's existence).
That it had a cause is a metaphysical principle, Craig would argue, since it is evidently true that nothing can come into existence without a cause. In addition, all (or most) the examples we have of beginnings involve causes and this is strong reason to look for a cause of the beginning of space-time and its matter content.
Craig would happily agree with that since he is proposing a non-physical cause. The alleged fact that physics breaks down there is reason to look for something metaphysical.
That's why I didn't mention the Big Bang at all. I mentioned infinity paradoxes, namely, the impossibility of an actual infinite existing in reality and the impossibility of the traversal of an infinite past. I also mentioned the 2nd law of thermodynamics, which is entirely independent of Big Bang cosmology. Even if there was a phase prior to the Big Bang, Craig would argue, it must have a beginning as well given these problems discussed above.
You have to prove it is a conjecture or speculation by pointing out problems with the premises or conceptual analysis, otherwise you're begging the question.
Well, I'll ask you to explain to us how the argument commits these fallacies. It is not enough to claim it is fallacious.
The argument is that since we know a subset of things that began to exist and had a cause, we're in our epistemic rights to believe that other members of the set (in this case, space-time, which is a thing) also had a cause.