I'd actually like to back up a step from there, if it's OK with you.

It seems likely to me that many of the items you list as evidence of the non-existence of the referent of "God" as understood by your form of Catholicism would also be evidence of the non-existence of the referent of "God" as understood by my form of Judaism. (For convenience, I will hereafter refer to those referents as the Christian God and the Jewish God, respectively.)

If that's true, it creates something of a problem, since while I would agree that seeking evidence for the nonexistence of X and failing to find it constitutes evidence (not proof, but evidence) for the existence of X, if the evidence you're seeking and failing to find is also evidence for the nonexistence of Y then failing to find it is equally evidence for the existence of Y. So, if the evidence you identified would demonstrate the nonexistence of both the Christian and the Jewish Gods, then failing to find that evidence would be both evidence for the existence of the Christian God and evidence for the existence of the Jewish God.

And the same goes for many other denominations' Gods.

Which would be fine, if your goal was to explore the existence of some kind of God, who might not be the Christian God... but it doesn't sound like that's where you're coming from.

And if X and Y are mutually exclusive, then the whole thing becomes rather a muddle.

So it seems it's important to find, not only evidence that supports the existence of the Christian God (such as failing to find evidence of Godlessness) but also evidence that differentially supports that existence, relative to the existence of other Gods (say, one of the Hindu Gods, or the God of some religion neither of us has ever heard of).

Would you agree?