I take issue with saying there's no proof, unless we always mean 'definitive proof' and never 'evidence with value' that God exists. If we mean 'definitive proof,' then believers will never be able to establish their burden. If we mean 'evidence with value,' then believers (strictly using Christians here) can point to (for example), Jesus, miracles, and traditional logical proofs of God's existence (think Thomas Aquinas).
It's nearly impossible, if not impossible, for us temporal beings to live up to a burden of definitive proof to show God's existence. After all, the original burden was on God, and even His efforts haven't had universally lasting effect (arguably not from want of trying, but because of our own damned stubbornness).