Reality is the interface of the senses. Our entire paradigm of understanding is rooted in an evolution tied to a specific environment. This is not to say that mysticism is valid in any way. If some "other" is beyond our senses and doesn't interact in the world circumscribed by them, it must be considered meaningless. It would be no different from fiction and its unknowable nature, being beyond sensory experience, would have no reference point from which we could contemplate it. Ultimately any "god" having the traditional descriptors (omni. . .) is self contradictory. Anything else would be limited. And if a limited version existed, it would need to operate in the world that we can sense to matter. If so, then it would matter as much as its effects and actions were beneficial or detrimental to our world.

At first I thought you were asking should it (god) make a difference and how. But you're asking what difference would it make if the existence of god could be proved? I doubt it would make much difference at all given that we now live in a post-truth world. There are plenty of things that are demonstrably true that people still don't believe.

Only if god communicates a wish or objective to us, a god who remains silent and invisible, a deist god, is no different from no god at all. Especially if as we have to suppose, it chose to remain silent and hidden.
Religions are, and were never, about the worship of gods, they are about the worship of holy books.

And since we have no evidence that any of the holy books was directly or indirectly authored by any deity, and a lot of evidence to the contrary, we can only presume that any deity who may exist, chose to remain silent. In which case, you could make a good argument, that religion and presuming to speak for a deity, is actually the most anti-god and unholy of all human games.

Yes, I've appreciated this site and hope it continues.

As to a god existing in reality, demonstratively proven, it wouldn't make a difference to me. I wouldn't change a thing in my life, at least not from what has been demonstrated to me so far in my life.

I'd say it's a pretty big failure on the part of a god who can't convey to its playthings how to get along in modern life, what the rules are so that we can understand them, aside from just our own social conscience.

So, if we are just to be here for the amusement of a god, watching us like a child might watch an ant farm, then we should just keep doing what we think is best and leave it at that.

Same back to you. Thou doesn't exist so no need to postulate the hypothetical.