Hi, long time Zelda fan, first time poster here. Grew up with the original games on NES and have played and beaten nearly every one, except TFH. I would like to give my own thoughts on this subject.
The fact that the name of Ganon exists, and the ruined Temple of Time, implies a Post OOT placement. We can rule out the Adult Timeline as this clearly classic Hyrule and not New Hyrule. Pre flood would not make sense either as "the hero did not appear". I doubt this game would retcon that so obviously (though SS did a few retcons of its own, to be fair). There may be other reasons the Kokiri turned into Koroks, but I don't think it was the flood.
The trailer gave us a big clue, in that it states that the history of the royal family is the same as Ganon's; this implies that this is not the first time they've had to deal with him. Either post TP, or anywhere on the decline timeline after ALBW makes sense here. One guess would be that this is a prequel to the original LoZ, explaining why that Hyrule is in ruins. And if the Master Sword is already in bad shape, and ends up being unusable by the end of BotW, that would also explain why it was never used in the original games. But I don't think this is the case, sadly.
The architecture we've seen suggests the child timeline. As well, the additions of the murals in TP HD suggest an additional story we have not seen yet. Aonuma has also hinted at this with his 'I see' moments. My money would be on a post TP game. With the Adult timeline effectively separate from the rest of the games now, and the decline timeline already pretty full, the child timeline would be the de facto default for continuing the story in a logical progression from OoT, TP, to BotW. Some time after TP, the Sheikah must have come back into prominence to build the technology we've seen, and a great civilization was built, until the spirit of Ganondorf somehow manages to return.
I don't believe this is TP Link, but an entirely new one, as the back story we've seen so far suggests this Link already fought against Calamity Ganon and failed. Many see this as the story of the Hero of Time's failure, which would have been cool to see, but the back story does not align with this, and remember that trailer line implies that Ganon has been a historic threat, not a brand new one as he'd been in OoT. So we have a new Link, who after failing in the back story, gets put to sleep for 100 years after Ganon is sealed, as a guarantee so that when the seal inevitably breaks that there will still a Hero to fight him. The Master Sword is placed to be protected with the Deku Tree, since obviously the Temple of Time is no longer suitable.
A wildcard here is that we do not know the state of the Triforce, or even if it will play a role in this game. Will be interesting to see if Nintendo can do more with it this time. That said the story seems pretty self contained and could fit in anywhere that Ganon has had a history.
Whew, those are my ranting thoughts! I know I've missed a few things, but this is what makes sense to me based on my experience with the series. Thoughts, criticsms, either way I would love to hear what you think!