what proof is there of his existence?
at least for yahweh, elohim, Jehovah or whatever name people prefer to use for him, theres a group of 66 books by around 40 different writers across 1600 years of various testimony to his existence, as well as other writings and archeological findings in existence backing up various events described in the bible
to my knowledge, everything about zeus (and other greek mythological gods, hindu gods, etc...) was simply fables made to explain the unexplainable without any eyewitness accounts or testimony to their actual existence
regardless, i dont doubt that other "gods" exist so to speak, even jesus is referred to as a god (a term that can simply be used to describe a mighty, powerful being). i personally believe in one true god almighty, to which the bible testimony shows that he frequently humiliated the "gods" of other nations, such as through the 10 plagues, or the challenge for baal to start a fire on a stack of firewood