For atla, I think if there was no wait for the avatar. Roku dies, Aang is born and is sent to the water tribes in secret once he masters air where he meets Katara and Sokka.
I think an atla version of a lot of things could be good, but most of all I want to see Korra where Zutara happened. You could wind up with a fire lord named Iroh who’s a waterbender.
I’m thinking the characters we care about are born a hundred years earlier. Kya is killed in the first strike against the water tribes. Hakota leaves on an immediate counter offensive to disrupt their naval supply lines as a newly appointed war chief. Ozai and Iroh are Sozin’s children. Very little has to be changed for Toph to show up. Basically the story goes from fighting an industrialized military that’s near victory to fighting one that’s just wrecking everyone’s shit and had just destroyed and scattered the air nomads. They’re still around in hiding and some have abandoned pacifism.
For the latter that’s what I think is interesting. The government was torn down and restructured after a fascist regime. I can’t imagine Zuko denying his child the title for being a waterbender, but I also can’t imagine that resulting in a stable fire nation. It would likely drive a lot of the conflict there.
What if: it was discovered, whether before or after Aang unfroze, that benders of other elements, and indeed even non-benders, CAN learn to bend said elements with enough effort and devotion? (e.g. A born Water Bender who isn't the avatar learns to Earth Bend, etc.)