There are a number of throwaway answers to that question that it might be tempting to give you. Perhaps if the moon were suddenly covered in flaming letters readable in every language simultaneously, or if the stars suddenly rearranged themselves to spell out a divine message, that would be convincing. Perhaps if God himself descended in glorious flames to tell me personally that he was there, I could be persuaded. And really, I could toss any of those out as the answer to the question, but I think it would be dishonest to do so. Because I don’t know that any of them would convince me.
After all, depending how these various revelations might manifest themselves, there could be natural explanations for any of them. These might range from hallucination, to natural phenomenon, to intervention by ultra-advanced aliens, to some explanation that I haven’t yet even conceived.
There’s this concept/joke in engineering: unobtainium (yes, the word existed before James Cameron created his MacGuffin for the Avatar movie). It refers to a hypothetical material that has all the properties you need in order to solve an engineering problem, except for the fact that it doesn’t (and often can’t) exist. It’s called unobtainium because it’s literally not obtainable, and that’s why appealing to it is a joke. I kind of see appealing to God as an explanation for a mystery as being like designing for unobtainium. Except that if I suggest that I can solve a problem with unobtainium, the other engineers laugh and then we go find a real solution. If I suggest that I can explain a mystery with God, large portions of the population not only take that as a real explanation, they will act as if it is nigh criminal to set that aside and go looking for a real explanation.
The thing is, no engineering problem has ever been solved by sticking with unobtainium. Nobody ever built a bridge or flew a rocket into orbit by throwing up their hands and declaring that it simply couldn’t be done until we discover unobtainium. And nobody ever made a discovery about how the world works by throwing up their hands and declaring the mystery couldn’t be solved without a god. All of our experience tells us that it’s irresponsible to declare “God did it,” and stop looking for any other explanation.
And here’s the thing: we will never discover unobtainium. By it’s nature, it’s undefined because it is literally whatever is needed to solve whatever problem you have. If we have a problem, and discover a material that solves it, that material will be something defined. It wouldn’t qualify as unobtainium. And God is the same way: the concept, at least in Abrahamic religions, has evolved to become the being that has whatever properties are needed to solve any mystery (and yes, I do mean evolved – the earliest portions of the Bible don’t really describe the sort of being modern Christians describe when arguing for their God). That means it is inherently undefined, so how would you ever identify it if you saw it?
So what it all comes down to is that I don’t see how I could be convinced to change my mind. I can only imagine it would have to be some sort of experience so emotionally overwhelming that it overrides the sorts of concerns I’ve raised here and elsewhere. I won’t say that it’s impossible that I might have such an experience, because absolute certainties are few and far between in life, if any exist at all.
On the other hand, all Abrahamic religions and many others as well feature rather prominently at least one character who knows absolutely what it would take to convince me: their god. I would think that an omniscient god would know exactly what would convince me that it exists, an omnipotent one would be able to do it, and an omnibenevolent one would want to do it. So maybe that’s in my future.
But I don’t think it’s likely.