I'm curious about how polytheists and neopagans determine which gods exist. Additionally, which historically identified gods from different cultures are the same entity worshiped under different names?
To clarify with an example, for those who adhere to the Hellenic pantheon, do all the gods of the classical Greek myths exist? Are those that exist the same entities as similar gods of other cultures (e.g., Zeus = Jupiter = Ahura Mazda, etc.)? How is this determined?
What does it mean for gods to exist?
Would you like a Biblical response? While I don't know which ones actually exist by name, there were originally 70 of them who did and who interacted with mankind. They are the ones described in these verses:
When the Most High gave to the nations their inheritance, when he divided mankind, he fixed the borders of the peoples according to the number of the sons of God. But the LORD's portion is his people, Jacob his allotted heritage. - Deuteronomy 32:8-9
God has taken his place in the divine council; in the midst of the gods he holds judgment: "How long will you judge unjustly and show partiality to the wicked?" - Psalms 82:1
The first verse describes the dispersion at Babel when God divided mankind into the original 70 nations (they're listed in Genesis 10). At that time he also disinherited the nations and inserted a layer of "middle management" between himself and us, with one "son of God" per nation. Each one of them was given a geographical territory and the people who lived upon it. He then created his own personal nation, called Israel, through the line of Abraham, Isaac, and Jacob.
The second verse describes how those gods governed us poorly, and the entire psalm is an account of God reading them the riot act. He stripped them of their immortality and prophesied that he himself would again, one day, inherit all of the nations.
That prophecy came true 2,000 years ago at the resurrection of Jesus:
And Jesus came and said to them, "All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit."
Those 70 sons of God, stripped of their authority over us, remain alive and active and are now humanities' enemies. They are the "principalities" spoken of by Paul:
For we are not contending against flesh and blood, but against the principalities, against the powers, against the world rulers of this present darkness, against the spiritual hosts of wickedness in the heavenly places.
So, did some of the ancient gods exist? The answer is "yes", although I don't know which ones. Are they worthy of worship? The answer is "no". Are they even to be interacted with? The answer is "no", because they have made themselves enemies of the human race.