After having finished the game's story, here's my take on the timeline including Breath of the Wild:
So, at the end of the Child Timeline, sometime over 10,000 years after Four Swords Adventures, running parallel to the original The Legend of Zelda (not necessarily exactly parallel in time, but it could be) but on a different timeline. I think the games makes this pretty clear, with Zelda's reference to Twilight Princess during her speech in the memory, and because she said that Ganon "gave up on reincarnation" before the Dark Beast Ganon fight. After FSA would be the only time in the timeline during which Ganon(dorf) was known to have been reincarnated (not resurrected), with a second Ganondorf appearing in FSA after the first was killed in TP.
Plus, the Child Timeline makes the most sense in regards to the races that are present in Hyrule in this game. The Rito still raise some questions, but there was that mural added to TPHD that featured Rito, Zora, and Young Link, so it can be assumed that Rito have existed prior in this timeline anyway, separate from Zora, and that Young Link's tales of his journey through time lived on in legend here as well. That could explain why the Zora King spoke of Rito as a sage and all. And remember, the inscription did specify "as told by King Dorephan" so for all we know it's not actually describing the events that really happened in this timeline, but rather the story told of the Hero of Time that lived on despite not actually taking place in this timeline, which was passed down as legend in the Zora royal family and elsewhere.
Of course, this doesn't answer how Ganon was freed from being sealed in the Four Sword, but any number of things could have happened in 10,000+ years' time, and the 10,000 year backstory is vague on how Ganon came back anyway. Geographical discrepancies (like the whole situation with the Great Plateau and Temple of Time) are also ignored, but at this point you just have to accept that locations aren't always going to match up exactly between Zelda games, I guess.