The following is not a question: Can something come from nothing?

[pocaracas]

Which just renders your initial "guess" all the more wrong.

1. How does that follow from what I said?

2. Note that I'm exploring various possibilities. If we can rule out an eternal singularity/whatever, then it had a beginning. Works for me either way.

There you go, again.
If you want to use a singularity, then the "eternal" part makes no sense.... Time is ill-defined at a singularity.... space too, so even my wording "at" is wrong.
All current evidence hints at such a singularity having happened some 13.8 Billion years ago.
Whatever existed before that singularity is unknown... It is also unknown if "before the singularity" makes sense.
What does it mean for something to start if time itself doesn't exist?

Too many unknowns abound when discussing the singularity... rendering any attempt to squeeze a god in there as a god of the gaps argument or argument from ignorance, which is, as we all know, a fallacy and, as such, should be avoided.
Because of that, please refrain from proceeding with that fallacious argument.