FOr many reasons I am going with the Minish cap. But the most obvious reason is because we learn how Link first got his green cap, as he starts the game with no hat just like the hero of men, Gustav........hmmmmmmmmmmmm
No offense, but this is why people make fun of people for using the hat as a timeline placer. Without a proper argument, the hat or lack there of is laughed at for good reasons.
The proper argument for the hat is as follows.
The hero in the BS wears no hat. It's important to note that the hero in the BS (a.k.a. the Hero of Men) is NEVER mentioned to be Gustav. That's just a misinterpretation that many players seem to believe. Gustav and the Hero of Men are given no connection in the game. It's gametrailers fault for letting people believe that. Anyway, the hero in the BS is most likely a past Link that has never appeared in a game before. If the Hero of Men is a past Link, then the fact that he has no hat is VERY important. It symbolizes that at one point in time there was a Link that wore no hat. Link in MC starts out with no hat which is symbolic in showing us that up until this game, it's quite possible that every past hero was hatless.
Bill Trinen who has spoken on behalf of MC has stated that MC takes the players deep into Hylian lore and can be viewed as the origin of Links hat.
The game focus' a lot on hats and to say that the hat dynamic towards Link's outfit is insignificant is disrespecting the creators of the game. The game focus' on three central hat themes.
1. The main item in the game stolen by Vaati is a magical hat that can grant any wish.
2. Ezlo is transformed into a hat that Link wears throughout the game and utilizes it's magic A LOT.
3. There is a lot of focus on the Hero of Men not having a hat as well as Link starting out hatless and ending with the gift of a hat.
Bottom line is this, to those who shrug off the hat theory, maybe you don't see it as much because all you see is a hat, not the symbolism behind it and the symbolism behind all hats in the game.