[forkerenok]

I think this is still workable with an expression/functional index, where the indexed expression is "happened_at IS NOT NULL".

[isuckatcoding]

Seems like a whole lot of extra trouble to be honest. What happens when you need to create a composite index?

[forkerenok]

You can do indexes that are composites of plain field values and/or expressions! At least in Postgres.

As for the trouble, I agree, it's a bit more involved.