EzekielRaiden
Follower of the Way
Magic. Specifically divination magic.Personally my view even in a setting where "Gods are canonically real and make their presence known in unambiguous ways." there is nothing to prove gods are anything other than just slightly more powerful entities.
Consider a zone of truth spell. The caster automatically knows whether the being in question passes or fails the save. Keep casting until they fail. Tiamat, for example, has a Charisma score of 29, for a total modifier of +9; she is not proficient with Wisdom saves. Presuming other deities are of a similar nature, that's d20+9 vs a DC of at least 8+5+6 = 19, meaning about half the time, Tiamat fails. We can thus assume that, for most deities, even if they cannot willingly fail the save, they will be very unlikely to pass it four times consecutively (and this could be improved further by using a powerful focus that adds to your DCs, having someone debuff the deity's saving throws, etc.)
At that point, they cannot willingly lie. Ask them if they are, in fact, a transcendental being, not simply a powerful supernatural entity, but whatever standard you prefer for something to be "actually a god" and not merely a "slightly more powerful entity." If the deity answers "yes" while affected by zone of truth, you then know that at least the being itself has no reason to doubt its own divinity.
From there, other divination magic to suss out the deity's origin. If they're not lying when they claim divinity, either they are crazy, honestly mistaken, or actually divine (Lewis's trilemma). Since insanity is usually not that difficult to identify from behavior, I think we can safely set that aside (some deities will of course also be crazy, but for the sake of argument, presume we keep looking until we find a being-claiming-to-be-a-deity that does not evince insanity.) That leaves an honest mistake, or a genuine truth. Divination magic can conclusively distinguish the two.
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This is why, in my own homebrew setting, I cut this path off at the pass. The One--the Great Architect--claims to be beyond all magic. Hence, by Their own claims and as They (or, rather, Their servants/proxies) admit, it is impossible for magic to answer the question; it cannot look back far enough, with enough certainty, and Their servants flatly reject the idea that any magic like zone of truth could ever bind the One. But magic is the only tool that ever could have answered the question in the first place, so the question is inherently unanswerable. Each sapient being must choose for themselves what to believe, and the One's explicit and inviolable policy is that They, and all of Their servants, will respect such mortal choices, even if that means eventual separation (possibly forever) from Themself (a fate which, Their servants claim, They would not wish on any of Their alleged children.)
The War in Heaven was specifically fought over whether to uphold all of the One's commands, including the command to never coerce mortals against their will (loyalist celestials); or just the overall Divine Plan but not the rule against coercion (the Rebels, aka present-day devils); or to throw out the Divine Plan entirely and just wreck shop because you can (the Destroyers, a mix of combatants from both of the other two sides who started enjoying the war for its own sake, for the rush of emotion and destruction, aka present-day demons.) Notably, all three sides claim to have won!
The party also knows there are at least two other distinct religious traditions, one of which (Kahina--druids and shaman) barely pays lip service to the One if they even care at all, and instead focuses on completely different stuff. The implication is that other societies also have their own ways.
I was very careful about setting things up this way. I want the question to be intentionally, overtly open. The power exists. Divine beings are distant but the party has seen some of the few direct interventions in the world. And yet the question is still, and always will be, a question of faith. It cannot, even in principle, be answered with scientific observation. No amount of data-gathering can prove or disprove the Great Architect's claims to being the monotheistic creator and sustainer of all of reality. According to the One's servants, that is exactly how They wish it to be. Because existence is beautiful specifically because it creates a tapestry out of all the different people and creatures and beliefs and actions present in it. To shackle this, even through anything as soft-touch as "reveal Myself in all My glory" type stuff, would be to devalue Creation. The One claims (or, rather, Their servants claim) that Their nature is incompatible with devaluing Creation in this way, so They never will, even though (in theory) They have the capacity to do so.