My personal headcanon is that it's been something like 5 years. I've been to all the settlements in the game so I've reconnected with all the major characters from BotW, so I'm gonna list some examples to give context as to how much time may have passed.

First are the obvious ones, the junior champions, Tulin and Riju. Sidon and Yunobo aren't a part of this conversation because we already know Zora have very long lifespans, and it seems like Gorons do as well, so they wouldn't visibly age in a handful of years. As for Tulin, he was clearly a kid in the first game, maybe like 7, give or take a year or two. That set of quintuplets seemed to be the same age as him, too, and the six of them now appear to be at least adolescent, or in their early teens. Based on Tulin being so headstrong during his quest, and the quintuplets being able to step up and take care of the village while all of the adults were off foraging, I think that supports the idea that they're becoming young adults. As for Riju, we learn that she had to become chief "at a young age," implying it was early that Gerudo usually take the throne, so I think she was probably around the age Tulin is now, in her early teens. Given that, she would be approaching adulthood now, making her 18 or so, which lines up with how she's clearly more confident and capable now, both as a leader and a fighter.

Speaking of the Gerudo, all of the little girls in the town have now aged up, and they look to be the same age Riju was in the first game. Maybe a little younger, but that could just be because Riju is the chief so she had a more mature air about her. I think they're the same case as the Rito children, going from around 7 to around 12. The last example I think is worth mentioning is Mattison, Hudson and Rhondson's young daughter. We all know we helped the two meet and get married in the first game, so obviously Mattison wasn't even a thought until after then, but in TotK, she's old enough to be taken to Gerudo Town, which apparently happens to Gerudo children born outside the desert once they "come of age." My guess is that means she's like 5, and that event is the equivalent of her beginning formal education or something similar. She may even be a bit older, considering how well-spoken she seems to be.

Having said all that, here's a bonus question, why the hell do Link and Zelda look exactly the same? We know Zelda was turning 17 from the memories in the first game, and it's safe to assume Link is close to the same age, so if a few years/half a decade has passed, they'd be over 20 by now. Though to be fair, I guess they're both over 100 if we wanna get technical so maybe they're just immune to physically aging after all the magic Ganon-sealing and nearly-dying mumbo jumbo they've been through.

TL;DR Tulin looks like he went from being a little boy to a preteen, and Riju looks like she went from being a preteen to a young woman. Likewise, the Gerudo and Rito girls have gone from being tiny munchkins to adolescents. Lastly, Hudson and Rhondson from Tarrey Town had a whole daughter who's old enough to be teaching herself the Gerudo language ahead of going to Gerudo Town because she's "come of age." Conversely, Link and Zelda uniquely don't appear to have aged at all, but they ARE special to be fair.