Great question and one that I think goes to the heart of the issue.
You ask:
what if there was suddenly a rift in the heavens and God said "Yep I'm here, see you in 2000 years!"
If such a thing happened, and if it was repeatable, and if it could be verified independantly, then I would say the whole issue of whether or not the existence of GOD was proovable would have to be reexamined.
But the evidence for or against the existence of GOD that is available today is simply not like that. It is not independantly verifiable. It is not repeatable. It is not subject to testing or objective measurement.
Science and knowledge move by disagreement and procedure. We advance our knowledge because two or more people disagree, but they have a set of procedures they can agree on that can then be used to sift evidence to arrive at a consensus. GODs existance or non-existance though is not something that can be tested by those agreed procedures. For one thing the very definition of GOD is such that the test can be manipulated by the subject itself to give arbitrary results. If GOD exists and is as most religions concieve such a being, he could have the tests end up anyway he wanted.
There are two other things involved. One is that what is seen as evidence of GOD is not repeatable. We have not yet found a way that miracles can be independantly verified, and if we did, it would strike at the very core of our use of the scientific method. If it was possible to violate the rules of physics at will, would they still be rules?
Second, so much of the evidence is subjective instead of objective. I look at the universe we live in and see an order, beauty and unity at the most basic levels that I believe implies a creator. Others simply do not see it that way. And for most things, whether or not that order is the result of creation is simply not important. Regardless, gravity still works, the four forces still function, time still moves in one direction, life evolves.
Aslan is not a Tame Lion