I concentrated on the computational power of God, but one can use other capabilities of God that the verifier believes no one else is capable of like omniscience or omnipotence, e.g. if God raises monthmount Sinai over my head and I hear a voice that says Torah is from God a few thousands years ago, I would be convinced (though others might not since they believe that what they see and hear is not enough, it might be magic or something).
One last point. Most rationals have been heavily influenced by science and only accept arguments that look scientific and are intersubjective. Say a personal interaction with God which is not intersubjective and reproducible might not convince such persons. AsloAlso arguments which appeal to other capabilities of humans which science does not understand well at the moment, a poem or a picture or a natural even can have a very strong effect on a human, but because science does not certify it they would reject that as a reasonable argument. But it seems that the sender/author of books like Torah or Quran does not share their idea and values psychological and literatural effect more than a scientific argument, maybe it is because science is changes too quickly too much, or probably he has a better understanding of how a human-being's mind works. Probably, these books should be analyzed from that perspective.