The contents of an atheist's mind?

If an atheist claims that she merely doesn't believe in God, she must have a reason, or else she's made a blind 'leap of faith'.

If she merely doesn't believe in God, she must therefore entertain the possible fact of God's existence. That is, the claim that she has no belief about God's existence, on her account, has nothing to do with reality apart from the reality of the contents of her 'belief-set'. Thus she must entertain the possibility that in reality there is God.

So what would overturn that possibility? What would confirm the belief as being true to reality or disconfirm it as being untrue, or, on the balance of probabilities that it is not true?