God doesn’t approve of incest. This is actually another easy one. It’s a statement of literal history, not of a position of God.
Sodom and Gomora have just been destroyed. God warned and saved Lot, Lot’s wife and Lot’s two daughter’s from the punishment sent to those 2 (5) towns by angels sent from God. Lot’s wife didn’t make it as she didn’t trust the Lord on the way. So only Lot and his two daughter’s survived the disaster.
They were hiding in a cave out of fear. We don’t know Lot’s position or state of mind at the time but his daughter’s assumed that the whole rest of the world had been destroyed. And they took it upon themselves to repopulate the earth with the only man that they thought was left; their father Lot.
Essentially, they got Lot drunk and became pregnant from him. That’s pretty much it. God didn’t say He approved of it It is in the Bible as literal history. In fact, by placing the story in the Bible, we see where other cultures in the region come from.
And back to the original claim that God approves of incest, when the Israelites had left Egypt, God told them of how close one could marry family. Incest is certainly not allowed.