Good morning, js1138! I'll take the second statement first: And thus Hawking is describing something the like of which nobody has ever seen in nature. (Thereby making the universe strangely "unnatural.") Or are you merely advancing this as an example of self-causation in answer to my question/request?
RE: your first statement: We do not see God directly as an object of nature. Thus He is completely unavailable as an "object of intention" and as such, not directly available to empirical tests. Analytical or instrumental reason -- apodeixis -- cannot find Him at all.
However, He is available to epideixis, a species of reason that seeks, not to demonstrate, but to say "go look!" This is reasoning by inference, in the sense that we find God, if we find Him at all, not directly as in the case of a physical object, but in His Word (revelation) and in His works in the natural world -- including His works in us -- which confirm His Word.
One datum He gives us cannot be verified according to the procedures by which we know objects of the natural world: In stating that He is the I Am That I Am, He certainly seems to be referring to Himself as eternal being. Thus not having had a beginning in Time. This is eminently logical: How could the creator of Time be the subject of Time?
But the universe, as creature, cannot make a similar claim. Which may be why certain cosmologists seem to have such a stake in making the universe independent of a beginning in Time, by denying that it is a "creature" at all.
It is true we never see God "face-to-face" in nature. What we see in nature are His effects -- His "reflection," if you will. These are (1) His laws, natural and moral; and (2) the beauties and wonders of this earth as structured by divine law, which in turn mirror the beauty, truth, and goodness of their Creator.
We all have a world view, js1138. Every last one of us: Every man has his "myth." These also are not available to empirical test. That is they are epideitic, not apodeitic: and only "by their fruits shall you know them."
apodictic
Apodeictic \Ap"o*deic"tic\, Apodictic \Ap`o*dic"tic\,Apodeictical \Ap`o*deic"tic*al\, Apodictical \Ap`o*dic"tic*al\, a. [L. apodicticus, Gr. ?, fr. ? to point out, to show by argument; ? from + ? to show.] Self-evident; intuitively true; evident beyond contradiction. --Brougham. Sir Wm. Hamilton.
epideictic
\Ep`i*deic"tic\, a. [Gr. ?, fr. ? to show forth, display; 'epi` + ? to show. Cf. Epidictic.] Serving to show forth, explain, or exhibit; -- applied by the Greeks to a kind of oratory, which, by full amplification, seeks to persuade.
therefore: apodeictic ~= beyond testing; epideictic ~= testible (about explanation) ...eh?