Seemingly, Sozin's whole plan was only useful to give his country like 20 more years max to win a war against literally the entire world. Even with perfect 100% efficiency, genociding the Air Nomads and detaining the Southern Water Tribe's benders would still leave an Earth Avatar, who now has been dropped somewhere on a massive continent you now have to take over before they grow up. Not only that, you'd risk creating a radicalised Avatar who could easily have beeen brought up with ideals more akin to Kyoshi than Aang to reflect the new realities of war. And so, any advantage you have on that front is gone in the next 20 years or so, unless you luck out incredibly and somehow capture that Avatar as well. Aang freezing was the (almost) best case scenario for the Fire Nation cause it gave the the most time, and they still blew it after failing to conquer the Earth Kingdom 100 years later (even though through part of those they were distracted bullying the Water Tribes).
Frankly, the far easier move when dealing with the Avatar would be to just let him come to you. Spend Sozin's Comet by celebrating a festival of friendship to show that you are still very wholesome and definitely trustworthy. Then just play the waiting game, building up your technological and industrial might in the process (which btw is pretty much the entire reason for all your nations' successes). Chances are that Aang would eventually come to your totalitarian surveillance state willingly to learn Firebending at some point.
And that's it, exactly the same result you wanted, only without paying the massive bill of destroying an entire people just to find one guy. Just imprison or kill Aang right then and there and then proceed with killing the incredibly corrupt and decentralised Earth Kingdom with stronger industry, better tech, and greater economic prosperity, cause between the pacifists and the isolationists there's quite literally no one else to stop you now.
And that's pretty much a foolproof plan, left unexecuted because one guy in a high place thought that he wanted his name in the history books by leading his barely industrialised nation to take on literally the entire world at once. I'm starting to think that the Fire Nation is way less an Imperial Japan type and way more just a modern Russia type, cause for all their mistakes Japan actually knew how to manage a military invasion.