If you have the custom ruler dlc then you can make your character a god through that. But I do not know if there is a possible God event.

I have the same question.

Okay, you're not SUPPOSED to be able to become a God without making a custom character.
This is because as a normal human, even if you have a child with one of the many God-Characters, you'll only get a demigod child. And even if you are a demigod and THEN marry a god, your children will still all be demigods. That being said, there's still a way to do it if you're very lucky.

It goes like this:
1.: Marry a God, for higher chance of success go for a master seducer/ seductress. This in itself is
tough, since the Gods are very reluctant to marry anyone except an emperor; same with court
invitation. I usually pick Aphrodite.
2.: Once you're married to a God, grant them a landed title so that they can pick the seduction
focus.
3.: Pray to whatever pantheon you believe in that your God-Spouse successfully seduces another
God and has an illicit child with them, WITHOUT exposing them, of course. And also hope that
that child is high in the line of succession, otherwise you'll have to do a lot of childmurder to get
that God-child.
4.: Wait for your ruler to die and play as an immortal, all-powerful God!

Yep, you have to become an Emperor and then get cucked by a God whilst being married to a God to play as a God. I mean, it's a small price to pay imho, but it's seriously tough to set up. It's way easier if you can find a God that already has another God as a lover, but that happens rarely.