The burden of proof isn't on the nonbeliever, it's on the believer.
The burden of proof is on the the person attempting to prove it.
If a believer is attempting to prove that God exists, the burden of proof is on the believer.
If a non-believer is attempting to prove that God does not exist, the burden of proof is on the non-believer.
Since the existence of God cannot be proved or disproved, attempting to do either will end in failure.
One can make arguments for and against the existence of God; most of these are logical arguments, rather than arguments based on testable scientific theory; but none of them can result in a proof.