I had a kid that was recruited for T&F that went to high end Ivy. They were recruited by the Ivies and other top academic D1 schools, as well as other schools.
I would not worry too much right now about whether to take the SATs ASAP for Ivy recruiting purposes. I think we all agree it would be very nice to get a good high SAT/ACT score early on, I am just saying I would not take the test earlier than you/your kid had planned for recruiting purposes.
I would just keep focusing on keeping the grades up and the academic rigor, which is the most important, and preparing well and doing their best on SATs/ACTs when they do take them.
I believe it has changed a bit now due to the NCAA rule changes on when a T&F coach could contact an athlete, though T&F recruiting may still be a little later than some other sports. Also, unlike other sports in which the level of competition can be a big factor so coaches need to see the athlete in action, T&F coaches can easily view the times online to see where they stack, so it is easier for coaches to find you.
When you start to focus the on the school’s that could be a good fit, I would reach out to the coaches by filling out the online recruiting questionnaire and see where it takes you.
Good luck.