We can't go into minds of Ancient Greeks and know it exactly, nor we do have certain direct answers but there are numerous examples showing they really believed in them and also examples of piety. These examples varies from them really practicing sacrifices and giving gifts to gods, stories like how Spartans were so pious so they did this and that on the battleground, people asking to temple of Apollo for their acts and if they should do this or that including serious decisions of setting up colonies, sanctuaries being highly regarded by Greeks, believing in curses, and even Athenians thinking Athena herself accompanied Pisistratus back Athens since the tall girl dressed like Athena in his chariot, not letting anyone to born or die on Delos since it was the island of Apollo and a sacred place, and such.

Things aren't myths to you if you're standing inside those, just like Jesus, Abraham, God's chosen people, miracles, angels, heaven, Muhammad going up to heavens, etc. aren't myths to people who do believe in the related sacred texts.