Seems odd to be putting things in spoiler tags in a thread marked for spoilers in the title, but maybe Mibbitable hasn't yet beaten the entire game. I won't talk about ending events except for a small snippet I'll put in spoilers, but anyways...
It seems this game takes place in the Child Timeline, much to my surprise, but it makes a lot of sense actually, given some of the story in the game. Namely, the original sealing of the Calamity Ganon, using Guardians and Divine Beasts. There's a hell of a lot of conflict with all other tales of Ganon being sealed away, since no other detailed event in Zelda history matches at all with the story of an army of robot octopuses and four animal mechs aiding the hero and the princess in a decisive battle to seal Ganon away.
That's where the child timeline comes in, because not once in that timeline was Ganon ever sealed away. Like it's been pointed out, he was never sealed away during Ocarina of Time's era; he was put through a failed execution and then sent to the Twilight Realm as a failsafe. Then when he came back, he wasn't sealed, he was just straight-up stabbed and killed. Fast forward many years later and we have Four Swords Adventures, where Ganondorf is reincarnated, again into the Gerudo tribe, finds the Trident of Power to become a powerful monster, and then is sealed... in the Four Sword.
Now, it's inevitable he escaped at some point, because come on, that sword sucks at keeping things sealed away. Vaati escaped at least twice on his own, in Four Swords and the backstory event that the same game references (which, as it turns out, is separate from the events of The Minish Cap). Sure, he escaped a third time due to Ganon's intervention, but give it some time, he would have escaped on his own again. Given this information, and how weak Vaati is in comparison to the King of Evil, yeah, Ganon's gonna break out sometime.
Whether the entity known as the "Calamity Ganon" is the same reincarnated Ganondorf from Four Swords Adventures or just a lingering manifestation of evil is unknown, but there is this tidbit towards the very end of the game...
Anyway, as was mentioned before, Zelda makes a passing reference to the events of Twilight Princess, which alone is enough confirmation for me. Sure, there's a lot of geographical references to other events on other timelines, but I mean, are you gonna take Nintendo going "Quick, let's name this area after a past game!" as concrete proof of timeline placement over a story cutscene? Nintendo likes to make cheeky references all the time; hell, Linebeck's outfit somehow appears in Tri Force Heroes, despite being on different timelines. Not that I consider that game canon at all so I just destroyed my own point.
But anyway, the simplest explanation would be that this game takes place on the child timeline in light of this. It's not at all what I expected, considering Aonuma's lines about this being a world that has seen multiple conflicts with Ganon, but three is still multiple (Ocarina of Time, Twilight Princess, Skyward Sword), plus the ones we haven't seen in that 10,000 year period, so his comment is still accurate. I suppose it's fair, it's been ten years since that timeline got some love, and I'm not exactly opposed to it. But it does beg the question of how did Kakariko go from a Native American style village to a straight-up Japanese village that's full of Sheikah instead of regular Hylians, this inconsistency has ruined the entire series!!!
I mean this was a good game.