God doesn't exist because He doesn't do what I think He would do if He existed.
That's anthropomorphism.
Well, if God did exist, what do you think he would do? How would one go about verifying claims of God's existence?
If you're talking about the Christian God, then we can use moral behavior to validate the claims of his existence since eating the apple gave humans the same ability to recognize good and evil that God has, so our views of that sort of behavior would have at least a passing similarity to his views of that sort of behavior.
For instance, if I see somebody raping a young child, I will stand back and watch while doing nothing to prevent it because I feel that it would be evil to interfere with the rapist's exercise of his free will. If I saw some sort of divine intervention occurring to spare the child getting raped, I would know that the intervener was someone other than God because God doesn't do evil things like preventing child rape.