Agree with most of the above -- on Sept. 1st they will text him/call him (even a few schools will send snail mail) if they are interested. Multiple texts from, for example, both the HC and RC.
One thing to check on the emails he's getting -- did the coach list his cell phone number (not office number)? If so, your son should call the coach's cell.
Agree with BaseballHS on Duke -- my son spoke with the RC (and I can only assume the RC spoke with dozens and dozens of others) in May of sophomore year, and they were offering kids they liked in that time frame.
IMO, you don't need test scores on Sept. 1 of junior year to get HA D1 recruiting interest. You will need them eventually, but just by way of example I know a current 2021 Ivy commit who hasn't taken the SAT/ACT yet. My son didn't take the ACT until Feb of junior year.