1. Canon I think points petty strongly to there being a period where Ozai favored both his children, before he decided Azula fit his idea of ideal offspring better than her brother did, but what if that wasn’t the case? What if Zuko were a sickly baby, or otherwise was imperfect in Ozai’s eyes? What if he wanted to rid himself of this flawed child? Ursa is horrified and also terrified for her baby. She goes to Iroh as the first born prince and heir, and he tells her to give the child to him for safe keeping. They smuggle in the stillborn baby of a pauper who couldn’t pay for a funeral, and tell Ozai that the baby died in the night. It’s this child, whose ashes lie in the royal crypt. Iroh intends to take Zuko to an army captain of his who he knows has been trying for a child, but then the army captain dies, and Iroh stumbles across a hidden ancient civilization, and long story short, Zuko ends up with the Sun Warriors.
Two years later, an unattended baby Mai crawls into a life raft while her family is traveling and winds up drifting onto the beach, only to be found, dehydrated and miserable by a Sun Warrior woman collecting shell fish.
2. Mai and Zuko have much much happier childhoods than canon, spending much of their time running around on the beach or in the outer edges of the jungle, climbing trees and cliff-sides, and scaring their parents half to death like many active children. They live just on the other side of the village square from each other, and they and the other Sun Warrior children grow up laughing, playing, and learning how to hunt, tend crops, fish, and weave. It’s just about idyllic, and neither of them know how lucky they are to have it.
3. At thirteen, firebenders among the Sun Warriors go to meet the firebending masters and present to them the sacred eternal flame. Zuko’s little brother has been talking non-stop about how the dragons are going to eat his brother. He’s also actually having nightmares, and he doesn’t want to watch, and Zuko is going to be sooooo glad when this is all over and Seiji can stop worrying. So when he goes with another thirteen year old to present the fire to the masters, he’s a little on edge. And then, something goes wrong. Ran accidentally burns Zuko. Everybody freaks out. Seiji is traumatized for life, Ran freaks out, and poor Zuko, screaming in pain, is picked up by a panicking giant dragon, and hidden away in her nest. He almost dies because she won’t let anybody near him.
After the worst of the fever is over, and she lets him out to shamble back home to the village, the elders put their heads together and decide that the dragons have obviously chosen him, and he’s now going to become their next high priest. Zuko is like, no, come back childhood free of responsibilities and big flying lizards who think they’re his mom, come back!
I should probably note here that dragons are not human intelligence level, they’re more like smart dogs.
4. As if the sudden invasion of a mated pair of dragons into his life, who try to parent him (and Zuko isn’t sure what he thinks about that, given that one of them burned half his face off, and then held him captive, and no seriously, he thought his brother was right, and she was going to eat him) his new teacher is Ham Ghao, and he is a bit of a… Instead of running around outside, he’s stuck tending the sacred fires and sweeping the temple floors, and the only person who keeps him sane is Mai, who shows up to sneak him out. Together, the two of them explore the jungle, gather fruit, and hunt for rabbit-dear and parrot-lizards. And as they get older, they find other things to do away from thr prying eyes of the village and Ham Ghao as well.
5. Izumi is going to be spoiled silly by her dragon grandparents, you have no idea. They’re going to keep bringing her dead animals and trying to teach her to hunt dragon style.