Alright I put this off long enough and I thought perhaps I should say what I have in mind when it comes to the main focus on this thread. Hopefully I may clear some thoughts or better yet, interpret my point of view in a different light.
1. Link's origin - Zelda had Hylia, and Ganondorf had Demise. They are technically separate characters, but were caused because of that deity. SS Prequel.
While Zelda and Ganondorf do originate from Hylia and Demise respectively, I don't think that's the case for Link. Zelda and Ganondorf are both able to use magical powers that what seems they have been known to have since the very beginning. And before you say "Well Link also can use fire, ice, etc.", he most certainly can...with the help from an item that is. We see Zelda and Ganondorf use magic that is generated from their bodies but we never see Link do so. He has to be using an item in order to gain the effect of using fire. And to take it one step further, I bring you Fire Mario. Now most people if not all will say "Mario uses an item in order to throw fireballs", while that may be true, Mario is able to physically generate enough energy from his own hands to make fire come out of his hands. So really the only way for Link to be considered to have fire magic is if he is able to generate energy to create fire from his very being, something we have never seen in the Zelda franchise.
Going back to the first few statements of the first paragraph above, though Zelda and Ganondorf have origins, Link does not. This is because unlike Zelda and Ganondorf, Link is mortal in the sense that he didn't have a higher deity that he originated from. In fact, I am willing to argue that the origin of Link and his future incarnations being once we gather all three pieces of the Triforce near the end of Skyward Sword. Also if this were a SS prequel, that means the game must focus on the origins of Skyloft, Hylia and Demise, and no Master Sword will be prominent in this installment. I don't believe that will be the case since if you look in the trailer we can see the area is very well established and if you observe carefully, you could see what appears to be Hyrule Castle or Castle Town, the area that Link and Zelda from SS were meant to colonize when they stayed in The Surface at the every end of SS. So with that stated, I don't think this will be a SS prequel.
2. WW Link's origin - WW Link was said to have no connection to the past hero, Adult Timeline had no Link during the great flood, meaning this person would be some new hero trying to save the land. Notice the shirt. WW Prequel.
I can never understand why people would automatically assume that one game in the Zelda franchise has to coincide with another simply because of what Link or other characters wear that similarly resemble another character's clothing in a different game. The reason why it can't be a prequel to Wind Waker is simply The Great Flood that was mentioned in WW's backstory.
The Wind Waker's Backstory said:
Long ago, there existed a kingdom where a golden power lay hidden. One day, a man of great evil found this power and took it for himself, and with it at his command, he spread darkness across the kingdom. But then...just as all hope had died, a young boy clothed in green appeared as if from nowhere. Wielding a blade that repelled evil, he sealed the dark one away and gave the land light. This boy, who traveled through time to save the land, was known as the hero of time. This boy's tale was passed down through the generations until it became legend.
And then a day came when a fell wind began to blow across the kingdom, and the great evil once again crept forth from the depths of the earth. The people believed that the hero of time would come again to save them, but the hero did not appear...
What became of that kingdom...? None remain who know. The memory of the kingdom vanished, but it's legend survived on the wind's breath.
On a certain island, it became customary to garb young boys in green when they come of age. Clothed in the green of fields, they aspire to find heroic blades and cast evil down. The elders wish only for the youths to know courage like the hero of legend...
Noticed the section that I underlined? Judging from the wording of the text, it seems the people of the golden land, Hyrule, were dependent on the Hero of Time returning to defeat the great evil. This leads me to believe that the Hero of Time
was the only one capable of defeating the great evil. Given the fact that The Master Sword is the only way to kill Ganondorf, this makes sense and thus means that no one within Hyrule stood up to Ganondorf, and thus The 3 Goddesses had to flood the land to prevent Ganondorf from achieving ultimate power. So if this game were to be a WW prequel, that means there is no Master Sword throughout the course of the game and despite what the player does throughout the game, Ganondorf will be victorious and The Great Flood will be the last event to take place in the game, leading up for Wind Waker to begin but seeing how Nintendo doesn't allow the bad guys to win, I highly doubt that will happen in this game.
3. Hero of Men - No hat, Hero of Men could've never been Link at all. U Protag has their hair in a ponytail, when undone it could look similar to the Hero of Men's long hair. Minish Cap Prequel.
Out of the three theories that you had in, I think this would make the most sense and even then there's a bit of flaws in your theories. First starters, you automatically assumed that it is a Minish Cap Prequel simply because Link wasn't shown with his hat. That means with that logic, Wind Waker, Twilight Princess, Spirit Tracks, and Skyward Sword should technically be prequels to Minish Cap simply because Link doesn't start with a hat but that's not the case. As far as the ponytail concept, it's plausible but I do believe the reason why Link has a ponytail is because he has long hair from the front and with him using his bow and arrow this makes sense as he would need a perfect viewpoint in order to shoot better. We don't know how long Link's hair would be if he were to undo his ponytail, but I personally believe this game will take place between Skyward Sword and Minish Cap but I wouldn't say that it is a Minish Cap prequel if that makes any sense. If it were to be a Minish Cap prequel that means the Four Sword will have to be a focal point at one point in the game in order for it to count as a Minish Cap prequel.