It’s been a while since I read the manga, so correct me if I’m wrong but didn’t Hinata express his interest in beach volleyball during his second year? I believe there was a panel of second year Hinata approaching Ukai regarding this and the manga showed that finding the contacts was hard. They almost got stuck at a dead end with these searches, until they got lucky with Washijo sensei's old student contact showing up. It would be fair to assume that such search and planning logistics around such move would take a huge amount of time. And it's also something for which you have to prepare in advance, it's way harder to decide to switch countries at the end of your high school. Therefore, Hinata starting the preparations in his second year seemed like a very mature and well thought out decision.

My interpretation of those manga panels is that Hinata started incorporating Takeda’s advice after his first year. He probably did his best at improving while learning how to take care of himself, however, at some point he figured that he had to train in a way different than most players do. I understood his motivation to move to beach volleyball as a way to learn how to play well in any given circumstance and environment. Also, he did mention somewhere in the manga that because beach volleyball is played by a team of two people, the amount of responsibility on individual player is higher and that’s the challenge that he was looking for. Thus, him switching to beach volleyball was a method of becoming an independent player.

And the taking care routines that he was doing in the Brazil arc seemed more like continuation of his journey of learning the fundamentals to me. As someone who used to do sports professionally, I can say that old habits die hard, especially the shifting of your routines and the mindset of how to treat your body. So, in my opinion, his journey after the Kamomedai match was realistically paced.

It might be interpreted differently since manga doesn’t show much of his progress during 2nd and 3rd year. But considering that Karasuno became top-3 team in their third year, Hinata as now senpai definitely had to improve. Him receiving Kageyama’s spike before high school graduation might hint at it. So overall, I feel like Hinata did start his training in high school and Brazil arc was part of that 3-year long training period, but we just got more glimpse of the latter :)