Proving the validity or falseness of an ancient religion is not exactly in the realm of history and historical study, any more than proofs of atheism or Christianity being right/wrong are. It is the realm of philosophy and science more so than history. It will be very difficult if not impossible for you to get an answer to your question as it currently phrased.

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As for the "factuality" of the Greek myths, you may be interested in When did the Greek myths "happen" from the perspective of the ancient Greeks? [...] by u/UndercoverClassicist which has links to previous answers of theirs about how much the gods were believed in the first paragraph.

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For the Egyptians, you may find Did the Ancient Egyptians believe that their gods were literally humanoids with animal heads, or did they believe that the representation was symbolic? by u/tweedy_impertinence interesting as it is talks about the relationship between the Egyptians and the "fantastic" representation of their Gods.

When did the ancient Egyptian Gods religion end? Is there any religion that has continued to worship them? by u/The_Manchurian talks about the decline of the Egyptian pantheon as a major belief system.

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Edit: re wrote intro to be less confusing and wrong.