Ocarina of Time is fairly early in Hyrule's history. There's a few games before it, but it's really the catalyst for most of the series. The time travel fuckery creates a split leading to three separate timelines. Nintendo won't confirm which timeline Breath of the Wild is on (I favor the "Child Timeline" of Majora's Mask and Twilight Princess, but there are compelling arguments otherwise) , but it takes place faaaaar after all other games. They set it 10,000 years in the future so they could basically soft-reboot the series without totally ditching the past lore. It can't be perfectly connected anywhere. But you have 10,000+ years to fill in with your imagination and make up for any continuity problems.
The way it ends on Jon's cackle is just perfect. I haven't enjoyed a BOTW playthrough this much since Ryan got shoved into the driver's seat in the Let's Watch series. Anyone else remember that? They managed to Shadow of the Colossus Epona within one episode, it was fucked up. And *amazing.*