Acolyte,
Hold it buddy. For all we know the tooth fairy or Roman gods could exist or have existed at one time. To say that because something has not been empirically verified, isn't logically comprehended, or isn't empirically testable, does not mean it isn't true. It's like saying because we have not seen a black swan, there are no black swans. At a time in human history Europeans would have only experience white swans and theorized they were white, but when Australia was discovered they learned there were black swans. This meant their theory about swans needed to be revised.
This is why verificationism, or the idea that our experiences guarantee our theories are truth-correlative, fell out of favor. Now science goes with falsifiability, which avoids this problem. We don't dismiss that black swans exist, but it's the theory we stick to until it's proven false (finding one in Australia).
Now God could exist. So could Santa Clause or Zeus. We can't disprove they exist, because they aren't empirically testable. Some ideas part of Christianity may be disprovable, but not God himself. Nonetheless, there is reason to prefer scientific theories over the God theory. At least scientific theories give us the ability to predict an outcome, and it does so way better than the God theory does mind you.
I simply just dismiss theories that are
1. Unable to be empirically tested
2. Are complex and are capable of being further reduced
3. Not supported by evidence
4. Not logically coherent
I limit my beliefs to theories that match the scientific criterion for very practical reasons, not because I assert they are truth-correlative.
But it's a mistake to assert that theories well supported by a large empirical database are
1. Truth correlative
2. Exhaust all other possibilities
Those implicit assumptions you are making are false and can be easily slammed down.