This game is beffore MC. Vatti's origin is in MC, Ganon's origin is in OoT. Both of which is after ZSS. But Majora's origins are still unmentioned. So it might be majora, but no chance of Vatti or Ganon. (I was so disipointed when I found out that the beggining of the ZSS trailer was just the history of zelda. No Mask Sequal? DX)
Nothing proves that this game takes place before The Minish Cap. That's a reasonable theory, sure, but it's not a fact. Also, while it is reasonable, it's not without its holes. Remember, the Skyward Sword becomes the Master Sword, not the Four Sword as it's implied the Hero of Man's sword became in TMC's backstory.
I agree Ganon is impossible. Vaati is still possible (at least me), since it has yet to be proven Skyward Sword will be a prequel to TMC.
Sorry, but I don't see how OoT fully explains his origins, as you claim. The only information about Ganon that we get from Oot is that he's first serving the king of Hyrule and that Zelda has a bad feeling about him. Nothing more. We don't see how Ganon even got into that position and why he turns evil/is evil from the beginning. Nothing is mentioned about Ganon's youth in OoT. And we even don't know how old Ganon is in OoT, there's nothing speaking against/for the theory that OoT's Ganon is actually a reincarnation of an earlier Ganon, therefore I wouldn't exclude anything.
Actually, there's more than that. Every 100 years in the Gerudo tribe, a male is born. That male becomes King of the Gerudos. Since the new king every 100 years automatically takes that place, it's safe to assume the old king is dead, meaning Gerudos live normal lifespans (besides, there's no reason to suspect they don't).
Ganondorf was that king during OoT. He was not very old; he was quite young. Furthermore he was completely mortal. Other than his magic (and there were lots of of other magicians in the game), he had no special powers until he obtained the Triforce.
It's unreasonable to me to assume he had any kind of significant past prior to Ocarina of Time... at least anything beyond a normal life.
You're confusing Ganon with Ganondorf. Ganon was created when Ganondorf touched the Triforce in OoT. That's as far back as his story goes, which is why I say he can't be in SS. What you say is true about Ganondorf though.
Ganon's existence is never explained. Nowhere does it state the Triforce created that form. It could simply be assumed he always had the power to turn into Ganon because of his sorcery. There's not really anything to go on there. The only place that ever explains his pig form is A Link to the Past, in which that was just his Dark World form. But that doesn't relate to the rest of the series at all... =\