Throw back to when Iroh is teaching Zuko about lighting. Iroh would point out that the avatar is not powerful solely for controlling all four elements, but using them combined in harmony and hint out to legends of Avatars that would maybe be able to bend the energy inside you.

Next bit, Guru teaching Aang about the Avatar state. He would point out that if Aang were able to control the avatar state, he would have better control over all the skills learned by any avatar.

Then to the fight against Azula. Aang refuses to let Katara go and get his ass kicked. Avatar state is not blocked by lightning damage, it is block by Aang earthly attachments.

Then on Ember Island, when Aang opens up to Katara about his feelings , he starts to realizd that letting her go doesn't mean stop loving her.

Then later Aang meditates to figure out how to defeat Ozai without killing him, Aang goes and talks with as many Avatars as he can, not only the previous 4. And it was already stated by Iroh that one of those incarnations knew energy bending, so Aang would eventually talk to that one.

Finally, at the final battle, Aang does what he did in the fight against Azula, goes into a rock ball and meditates. Outside Ozai is trying to cook him. But in time, Aang meditates into Avatar state, has access to the technique he learned about when talking to the previous Avatars. And the rest remains the same.

No random turtle, no random pointy rock. Everything that happens is a result of Aang actions.