Ok, there are somethings wrong with that argument.
1. It does NOT show Ganon at ALL in the game in any way shape or form. The monsters are what the Hero of Men (Gustaf? Just NOT Link, though maybe SS will disprove...) saved Hyrule from. And the Ganon you saw is a Moblin. Did you play Wind Waker by chance? or Ocarina of Time? Just go to the Forsaken Fortress/Ganon's Tower, or the Lost Woods in the future.
2. You are right that him getting his cap doesn't prove anything, but that hardly supports your point by complaining about it.
3. You plainly saying this without proof is not helping anything. If anything, it makes me want to believe the opposite (though I admit I may be biased that it is first due to my timeline theory)
Here's my reasons on why Minish Cap IS first.
1. Hyrule has only been partially united, shown by a small Castle Town, a Lake Hylia closer to the source and with less erosion, the Gorons finding a cave to live in (though that may be a clue for the antithesis), Death Mountain not having formed yet, no desert, and every sprite of the game's characters (excluding Beedle's) has the pointed Hylian ears.
2. There is no mention of the Golden Power, Golden Land, or any war. The War of the Triforce is a pivotal event that takes place pre-Ocarina of Time, as it is when Link's mother is wounded and gives her child to the Great Deku Tree. If it had taken place post-war in any way, it would have mentions of it. The Royal Family's tomb having the pots shaped in a triforce and the royal family's seal may show that it was merely a legend they all believed in.
3. Ganondorf is not so much as mentioned or even hinted at in the game. If the game came after OoT, the people would probably have at least legends of the evil one.
4. Again, no hero pre-MC Link wore a green cap, and it seems likely that the people would idolize that Link for saving Hyrule and would feature him with a green cap from then on.
5. A war seems to start at the end of the game, with all the people beginning to fear the monsters. this may be the trigger to the War of the Triforce.