You can in fact prove the non existence of a thing that is logically incoherent. Obviously the default position to be is agnostic, but you can actually disprove the existence of specifically a tri omni God via the problem of evil.
If an all knowing, all powerful, all loving being existed, we would not observe evil in the world as it would be knowledgeable enough, powerful enough, and care enough to get rid of it. We observe evil, so this being does not exist.
Of course, a lot of behaviour of God in the bible suggests that he is not all loving, which would trivially resolve the paradox, but a lot of Christians believe in a tri omni being anyway, which makes my prior argument non entirely irrelevant.
You can’t prove the non-existence of the god(s) that today’s religions worship, because their goalpost is always moving and logic isn’t in their belief system. That’s because religiosity allows someone to suspend logic and rational thought. This leads to someone believing in illogical things as fact, even if fact hasn’t been established.
Yes, the fact that evil exists would prove that an all-powerful, loving god who will do anything to protect “his children” doesn’t exist.
But then the religious folk would say, “evil things happen as part of God’s plan.” and that shuts down your evidence. It’s always like this, because faith is quite literally “believing in the absence of evidence”.
It’s super easy to disprove, for example, the “power of prayer”, but the person claiming that prayers are answered should be the one to prove this, in a way that can be tested and verified.
