Kids are like sponges, they absorb everything and you don't realize it until you squeeze it.

My cousin's daughter lives in a place where English is not used much, yet her mother who teaches it at a school used it with her everyday, and had a similar experience where she one day spoke fluently (for a kid) with no effort.

Maybe some kids just need to find the little "cognitive bridges" that make the language functional to them, then they can just use it, almost like they unlocked a whole dictionary in one hit.