As soon as they open the applications for NROTC. The boards will typically start meeting for NROTC in the end of Aug./early Sept. They go by 1st come 1st boarded. Many kids will have their applications submitted sometime in July.
If your DS has not taken the SAT/ACT yet I would strongly suggest he take as often as he can this spring and take both because some kids do better on one compared to the other. Plus, some kids do better on one test compared to the other. Aim for high 1300's or 30+ ACT composite to feel competitive. Note: I said competitive, not safe. There is no such thing as a guarantee for either, but the closer you get to that 1600 or 36, the higher the chances will be for getting a scholarship, if they are competitive in all of the other portions.