Some people say that atheists wouldn't accept the existence of God if God himself personally came down to verify his existence. I don't think this is accurate. In fact, I don't think God would need to even go that far to prove his existence to me. Here are some pieces of evidence that we could discover in the future that would make his existence more likely to me. organized from most plausible to least plausible:
1. If we discover that time predates spaceOne of the primary issues with a Creator God is that it implies a causality either without time or before the universe. A "first cause" would still need time to exist in, as far as we know. However, there could be a "first cause" for the 3 spatial dimensions as a product of the temporal one, and this might be decent evidence for the existence of at least a minimally-defined Deist God.
2. If we discover immaterial mindsAnother issue with the existence of gods or spirits in general is that, as far as we can tell, minds only exist as an emergent phenomenon from matter. How could something that predates matter and all of the fundamental forces have a mind? If we could show this to be possible, it would also provide some evidence for God's possibility. Some theories of Panpsychism like the Cognitive-Theoretic Model of the Universe might prove fruitful here, but CTMU would have to demonstrate a functional Theory of Everything to show its veracity, in my opinion. If it does that, it would provide good evidence for a Pantheist God.
3. If Enochian magic could be used to falsify physical lawsThe idea behind Enochian magic is that Enochian is the language that God spoke the universe into existence with. This actually isn't too far off from some theoretical concepts of a "mathematical universe" or "mathematical monism" where all of reality is an emergent property from some sort of algorithm, essentially a computer simulation of a virtual space. If the code is written in Enochian, and we can hack the source code of the universe, then I think that would provide some evidence for the existence of God given that Enochian was supposedly given to man by angels on behalf of God. Currently, though, "evidence" of the efficacy of Enochian magic is indistinguishable from magical thinking and apophenia.
4. If we discovered that prayers somehow transmitted into space using a form of previously-undetectable waveIf we discovered that prayers specifically act as some sort of transmission on a layer of reality that is ordinarily invisible to us, then that would be evidence that prayer might genuinely be communicating with something. Whether that something fits theological concepts of God or not, I would be comfortable saying that whatever is receiving those transmissions is essentially acting in the place of God and could take that title as the object of prayer.
5. If we make contact with life after death and they affirm God's existenceWhile this would not be direct evidence of God, it would be good enough for me. If we somehow discovered a way to talk to spirits of the deceased, not only proving the existence of an afterlife but proving that there is a ruler of the afterlife, then that ruler could be considered a god.
6. If we proved Young-Earth CreationismIf Young-Earth Creationism could actually verify its claims, then it genuinely would provide evidence that humanity was spontaneously generated by the hand of God. To do this would be a massive undertaking. We would have to prove that the Earth (and the rest of the universe) is only 6,000 years old, that humans are a product of spontaneous generation and not evolution, and that all of humanity descended from a single pair of humans. However, if we could prove that a literal reading of Genesis lines up with the facts, then that would seem to indicate that whoever wrote Genesis probably knew what they were talking about.