Suppose an atheist accepts the conclusion from the earlier stage of the argument, and agrees that indeed the non-existence of GOD cannot be proved. Yet, that atheist would argue, this is no reason to believe that GOD exists because such a belief would require evidence.
Since there is no evidence proving the existence of GOD, the rational choice is to believe that GOD does not exist. In the same way it can be said that it is impossible to prove the non-existence of Santa Claus. But it is not logical to believe this culturally accepted character exists just because its possible existence cannot be ruled out. Accordingly, those wishing to prove GOD exists bear the burden of proof.