-TMC is before FS/FSA, but FS/FSA seems to place itself immediately after OoT in my estimation

-Not only does Link not have the hat but the hero of men didn't either

-Wind Tribe seem to be early Oocca

-Hyrule has not been unified (Death Mountain isn't even a feature)

-End Sequence says it was Link's first adventure

-most importantly, the Minish are responsible for the construction of Armos Statues, creation of Pegasus Boots and hiding items under rocks and things. If the Minish came through the door in Hyrule Castle, then it wouldn't have survived the flood. So you have the dilemma of either the Minish arriving after the flood even though OoT features their handiwork, or they arrived before OoT and Hyrule Castle somehow survived flawlessy, Minish Door and all, through the flood until the time that post-flooders place TMC.

Now alternatively, you could say that TMC is late in the Child Timeline, and I couldn't argue with you, but noone ever seems to hold that opinion.

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My Timeline Theory

Zeldas completed:
LoZ, AoL, ALttP, LA(DX), KnS, OoT, MM, OoS, OoA, TWW, FS(only on Silver Keys), FSA, TMC, TP(Wii), PH.
MAN I love the Zelda series.