Back in the late 80s, I went to one of the best public high schools in my metro, and while most of our top students went to our flagship university (one of the very good ones), or maybe a more local LAC, some went to Ivies, MIT, other “national” universities and LACs, and such.
I knew test prep classes existed, but at the time, at least at our school, that was considered something you might do if you were bad at tests. If you did well enough on the PSAT, you just went ahead and took the SAT, maybe doing some practice questions first. If your SAT result was bad enough, you might retake, and might get help, but most of us got SAT scores we thought were good enough on our first try, without a lot of prep.
And that made some sense because the SAT scores you needed to get into even the most selective schools at the time were not that crazy high. My S24 laughs every time I remind him of the SAT score I used to get into a very well known college. And then when I mention my HS GPA, I think it nearly turns to tears . . . .
Of course I have no idea what was going on around the rest of the country, and for that matter it is possible some peers did classes or a lot of practice tests without me knowing. Still, I think it is fair to say the norm today of very good test takers planning to do a lot of prep and multiple rounds of tests to get the best possible score did not exist in my HS at that time.
But that is the norm now, and so I think the OP does need to plan out a possible process like that in advance (understanding you can still stop “early” with a good enough score).