It stands to reason, at least to me, that it is logically impossible to prove God's existence or non-existence using evidence that humans could perceive, as this evidence would be, logically, created by such a hypothetical God in the first place. Game pieces proving the existence of the board game designer and all.
The religious claim is that the designer is in some sense "in the game." That does not imply the possibility of provability, but it does imply the possibility of perception - and therefore, evidence, (though perhaps not to standard scientific methodology).