On my level, the philosophical level, it’s not “no God,” but “no ‘therefore God’.” In other words, because “God” has not been the conclusion of a sound argument, it cannot serve as the premise of any sound argument.
Are we? Methinks that remains to be seen. But at least we philosophers know that we know nothing…
Not impossible per se, just unthinkable for us… Like your Gensler’s “all A is A”, non-contradiction is “an axiom, a postulate, or a tautology”, as my Gemini put it.
You are, though; just a Catholic suffering from hemiplegia:
I’ve come up with an Ichthyst version of “the cogito”:
Deum esuriunt, ergo est.
You can go ahead and take full credit for that one.