The distinction between whether or not there is evidence is crucial to your position. Now you're doing the cop out thing which is: there is evidence, but we can't detect it yet. That scenario is indistinguishable from no evidence. But as long as you don't admit to no evidence, you don't have to admit to no god.
But if you're saying even no evidence=possibility of god's interference, you're by definition wrong.
But if you're saying even no evidence=possibility of god's interference, you're by definition wrong.