Potential spoilers ahead.
In an interview posted today with several key members of The Legend of Zelda: Tears of the Kingdom's development team, series producer Eiji Aonuma let slip a key detail that may finally cement the game's place in the Zelda timeline. While speaking on the game's theming around the concept of hands Aonuma made the following comment.
"Well, simply put, "hands" expresses the idea of "connecting." This applies to the story too, which connects to Hyrule's past. It also talks about a major struggle called "The Imprisoning War," which until now was considered a myth even in Hyrule."
The Imprisoning War is an event which, according to the official Zelda timeline, takes place at the start of the Fallen Hero Timeline. In this timeline, Link fails to prevent Ganondorf's rise to power in Ocarina of Time. As a result, the seven sages have to gather an army and fight to finally seal Ganondorf in the sacred realm.
It has long been theorized that Breath of the Wild, and by extension Tears of the Kingdom, take place in either the Fallen Hero Timeline or the Child Timeline. Others have postulated a joined timeline, but this was largely based on a poorly translated Japanese website for Breath of the Wild.