You ever watch the NFL scouting Combine? It's a stat every recruiter looks at for most sports. As a competitive volleyball player I (and my coach) obsessed over a 5% increase that came from years of training.
The evidence that you can train for the SAT is pretty scarce.
https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1745-3984.... https://nepc.colorado.edu/sites/default/files/Briggs_Theeffe... https://slate.com/technology/2019/04/sat-prep-courses-do-the...