Question

What would have to happen to disprove the Rabbi’s belief in Judaism?
I think the Rabbi once mentioned that if he reached a logical conclusion that God does not exist, he would follow that conclusion. Am I right?
Are there other things besides a logical conclusion? (Just for the sake of discussion—for example: hidden cameras whose authenticity cannot be disputed are discovered aimed at the site of the revelation at Mount Sinai, and when we run them back 3,000 years we see absolutely nothing—would the Rabbi fly to India that very day?)
 
P.S. The title expresses the fact that there are many religious people who will believe no matter what happens, and if nothing can ever disprove their belief, then it doesn’t really exist.
Thank you very much for the response, and Sabbath peace