There is an Avatar TTRPG and it faces similar problems to making a new game based on the series, and handles it similarly to what you're suggesting.

The TTRPG divides the setting into Eras, Kyoshi era with the nations still being established, Roku era with established nations, The Hundred Years War era taking place during the war but before Ang wakes, The Aang era, after the show and its sequel comics, and the Kora era taking place after TLoK and its comic trilogy. Notably, none take place during the events of the main series. This means that the can create new stories that better fit the medium and don't break cannon, and at the same time, you can still interact with significant characters and tie your story into the cannon such as making a quest resulting from the reprocusions of, or a prerequisite for events in the main canon.

Edit: clearly none of us read the article:

It'll put players in the role of an "all-new, never-before-seen Avatar" and take place thousands of years in the past.