Definitely apply early - nothing to lose and everything to gain.
You need to have taken your SAT's so I would suggest that a Junior take them in January then you have time to take them again in May or June.
Some planning is definitely required.
This is a sketchy timeline. The CNET board that determines scholarships begins monthly meetings in August until March or April. The highest volume months are after the new year but some units can be filled by Christmas.
Once your application is finished it is reviewed by a local NROTC recruiting unit who will contact you for an interview. After they approve you it is sent on to CNET and can take up to two months to before it is on the table for their judgement.
My son finished his app in late October and was contacted by the local review office w/in 24 hours. He interviewed two days later and was awarded an ISD. He didn't receive official CNET approval until late January.
The approval showed up on the NROTC website. His congratulatory letter came in April I think.
His app was actually held up by our local high school who couldn't get his transcripts submitted in proper format or to the correct email/physical address. (It's a very good high school w/ a conscientious administrator but things can happen.) It took persistance and several phone calls to figure out where the tangle was.
Getting the app done soon is also a good idea if you will be juggling sports and challenging classes as your personal time wil be very limited.
This is to the best of my memory - other people here may have more accurate info.