User blog comment:Rassilon of Old/Young Justice spoilers at Comic-Con 2012/@comment-4967138-20120805211615/@comment-1038387-20120808125208

Well, technically, only Zeus is a Greek god. When he was created, he got his powers from the Groman gods - it wasn't until War of the Gods (1991) that the gods of Rome and Greece were established as separate entities.

How did he become Captain Marvel:

Billy Batson was orphaned at an early age, and his uncle Ebenezer cheated him out of his inheritance. He lived on the streets and in shelters, and made a living as a newsie. One day, a mysterious stranger in a trenchcoat asks him to follow him into a dark and abandoned subway station where he gets on a funky subway and the Wizard Shazam tells him he's the chosen one for all these awesome powers.

Jerry Ordway's modern reboot has added a couple of things: first, Theo Adam (a reincarnated Teth-Adam of sorts) is responsible for his parent's deaths, and second, Shazam makes the stranger appear like Billy's father to gain his trust. Because yeah, by the eighties, they figured letting a young boy follow a complete stranger was not really setting a good example.