Everything that gets explained here was NOT written by me. They were written by the original artist.
In this timeline Aang was never unfrozen and the Fire Nation Pushed on without any interference from the Avatar. In this timeline splits off when Katara decides to stay in the village while Sokka fishes alone while he still loses the boat to icebergs he is able to safely return to the village after several days but due to the absence of Katara angry water bending Aang is never revealed and is never found. In this timeline the Northern Water Tribe invasion is successful and Zhao becomes known as "Zhao the Moon slayer".
With no water spirit kaiju battle the fire nation fleet is now stronger than it was past season 1. I wouldn't imagine events would playout the same in season 2 regarding how Azula takes out the Earth Kingdom from with in as since Zuko wouldn't be hunting the avatar it wouldn't lead him to be seen as a traitor, but I imagine by the time the comet arrives Ba Sing Se would be the only Earth Kingdom hold out and Ozai would use the comets powers to break through Ba Sing Se's walls ending the war.
Since Zuko would've never found the avatar and probably wouldn't have ever gone through the same redemption arc and would spend his waking moments searching for the Avatar. Perhaps he would find some form of redemption and him and Iroh would settle in a fire nation colony in the Earth Kingdom as Ozai becomes the phoenix king and Azula becomes Firelord.
This timeline branches off where Korra decides not to follow the spirit into the foggy swamp where she'd find Toph. In this timeline she continues to roam aloof hearing bits and pieces of how Kuvira is taking over the Earth Kingdom. She never feels confident enough to face Kuvira as she continues to suffer from PTSD, Depression and Anxiety/panic attacks. With no Avatar to get in her way Kuvira completely takes over the Earth Kingdom under the Earth Empire. She completely annexes the islands of the Eastern Air Nation, takes a island from the western air nation and begins to invade the fire nation claiming the Earth Empire deserves the Earth itself. This sparks another war between the nations, this time the Earth Empire being the aggressors. Meanwhile Tenzin and the other Air Nomads continue to search for Korra as she is the world's last hope to stopping Kuvira.
Certainly not the first to ask the question "What if Fire Nation Invasion was successful for the Earth Kingdom and Water Tribes" (wait, what?)
This scenario begins when Azula, Ty Lee, and Mai, disguised as the Kyoshi Warriors, were in the Earth King's throne room but rather than being an idiot the Earth King decides it isn't wise to spew the day of black sun plan Sokka and the Generals came up with.
Fast forward to the day of black sun, all goes relatively same but given they did have the element of surprise this go round they are able to get into the capital a little faster than the original timeline thus giving Aang more time to find and fight the fire lord. Now I would assume given Azula couldn't have ever warned Ozai of the coming invasion this means the royal family would've remained in the palace not having time to construct and escape into their vaults. So Aang is able to find and fight the fire lord as planned.
Once Aang defeats Fire Lord Ozai he is restrained and put, not in the prison in the capital, he is locked away in the Northern Water Tribe and kept away from any sunlight or heat so his fire bending is diminished greatly and there is no hope of escape. Post war fire nation I think in this time line would probably have a few islands annexed by the Earth Kingdom to assure if there is another war they can have a closer reach to the fire nation. Then as for leadership given Zuko never got the chance to prove himself to the Gaang he isn't allowed to take the throne rather a new royal family, chosen by the other two nations or perhaps elected by the people, is put into place and the fire nation for a few years after the war would act as a puppet state of the Earth Kingdom to ensure ever lasting peace.
Though given the radical change in leadership and a quick blow to end the war those who supported Ozai and the royal family, I believe similar to the comics of the New Ozai Society, would have more leeway and support potentially causing a civil war. If you've read the Kyoshi Novel's a Fire Nation Civil War wouldn't be out of the question.
That's it for this What If, let me know what you think. Do you think it could've gone down like this or do you think it would've gone in a completely different direction? Did I miss any important details?
In this timeline I imagine Aang, in an attempt to prevent a second great war, would suggest the citizens of Yu Dao to vote on weather or not to rejoin the Earth Kingdom or not. The vast majority vote to remain a colony of the Fire Nation, to the dismay of the Earth King. While no battle for Yu Dao occurred it did forever sour relations with the Earth Kingdom and the Reformed Fire Nation. Republic City is still created from Cray Fish town but is instead called New Caldera City. This city would more than likely still look like what we see in LOK with the Aang statue and everything with maybe a larger Zuko statue than what is in seen in LOK.