Crackpot theory time!
Botw takes place before the timeline split.
You may say "but ganon!" Ah, but you see, this is not ganon as we've seen him before, this is the calamity ganon, it later is reborn in ganondorf, who then becomes the physical manifestation of the calamity when he gains the ToP, this is the original hyrule, the one vaati terrorized in minish cap, it is completely destroyed by calamity ganon and the country is rebuilt by the time oot happens, this not only explains the temple of time is still standing, it's not the same temple, but also why the master sword isn't in it, as well, hyrule is a lot smaller in any other zelda oot onwards.
Or, y'know, it takes place before tp.