Miyamoto said somewhere, prior to TMC's release, that he considers Four Swords to be first.
Since TMC and FS are able to effect both timelines, it's possible that we might see Vaati in another game in the Adult Timeline. They might do that with Spirit Tracks, though it's doubtful.
One thing I want to ask is: what in The Minish Cap, other than moblins, clearly states that it's NOT before Ocarina of Time, as the first post mentions? I don't think the moblins are another form of Ganon or whatever, so saying anything about that won't convince me.
for starters, i want to say that i believe that MC is the first game in the timeline. i am still rocky on where i would put FS but i do believe that MC is first in the timeline. everything i am about to say isnt because i dont believe thats where it goes, but its just to answer your question and play devils advocate.
reasons as to why MC WOULDNT be before OoT.
1. you already mentioned moblins and people believe that moblins were made by Ganon or something like that (i dont like this reason).
2. the fact that when you look at the map and its the zoomed out map it shows two islands which is a sign of an ocean which COULD mean that it is right after the flood before WW or it takes place not too long after WW.
3. the mentioning of the triumph forks in the library in MC. in WW, the fish would talk about triumph forks which was a messed up way of saying triforce. in MC, there is a book in the library and im not sure what the book actually says but i know that "triumph forks" is in the book. this implies that the game comes after WW which is the only other game to mention triumph forks. (many speculate that the mentioning of the triumph forks is just an easter egg and nothing more).
4. when you get the figuring that talks about din, nayru and farore (the girls in MC that resemble the goddesses), their descriptions say that they are descendants of a line of oracles from Labrynna/Holodrum which is evidence that MC is actually supposed to take place after OoX (which CANT be before OoT). a counter argument to that is that the oracles in OoT could be descendants of the girls in MC which would then mean that MC could still be before OoT.
thats pretty much the only decent evidence for it to not be before OoT.
reasons why it could be before OoT:
1. no menioning of Ganon/dorf WHATSOEVER. its the only Hyrule based game to not have ganon/dorf in the game. this implies that no one knows about Ganon/dorf, he hasnt been born yet, etc...
2. the BS of this game does not seem to resemble any other Zelda game and also talks about a hero that seems to NOT be Link. this implies that this is the first Link to have an adventure.
3. this game seems to show the origins of the hat.
4. the hero of men captured monsters and locked them in the chest with the four sword. when Vaati opens that chest, he releases the monsters. this might explain why there are monsters in Hyrule throughout the series. kind of like a pandora's box idea. ill explain.
evil was sealed away in a box. pandora was told not to open that box. she did and she released evil onto the world, but she also released some hope, as well.
monsters were sealed away in the chest. Vaati was told not to open that chest. he did and he released monsters onto the world, but by opening the chest, he left the broken sword which was the only weapon powerful enough to stop him. so in essence, the four sword was the hope that was released with the monsters.
basically, it could explain why there are monsters in the world of Zelda.