If not Thor, would you accept Marvel Comics' Hercules, formally introduced in Journey Into Mystery Annual #1, in 1965?
Mythologically speaking, he's more of a hero and merely a demi-god, but he's certainly a mythical figure that found its way into popular (comic) fiction two years before Star Trek's Apollo.
A second possibility, earlier but a bit less concrete, can be found in C.S. Lewis' Narnia books. The books are mostly comprised of Christian allegories, but with plenty of other mythological tidbits thrown in for good measure. One that specifically comes to mind is in Prince Caspian, way back in 1951, where a wild Bacchanalian party is thrown by, well, Bacchus himself.
One was a youth, dressed only in a fawn-skin, with vine-leaves wreathed in his curly hair. His face would have been almost too pretty for a boy's, if it had not looked, so extremely wild. [...]
"I say, Su, I know who they are."
"The boy with the wild face is Bacchus"
The reason I say "less concrete" is that he isn't really a central character, hardly a character at all. He just shouts out his "Euan, euan, eu-oi-oi-oi-oi!" and inspires a moveable feast around him, but isn't much more than background.