At any point. No standard that is outwardly visible. The SAs use these in any way they wish, at any time, for any reason, in any number, they deem appropriate to meet class-building goals. In one sense, as Admissions starts reviewing data coming in from candidates, they evaluate all for LOAs.
Your goal is the appointment. The majority of USNA midshipmen never received an LOA. As is often said around here on SAF, the LOA is a unicorn. If one happens to wander into your portal, rejoice, but don’t spend any energy looking for one or trying to hunt one down. And, do not spend any time wondering why another candidate got one, and you didn’t, and you know you have a better X score or Y attribute. You don’t see the totality of their application. Focus on what you can control.
Invest your energy in submitting the best application you can, tending your alternate plans, enjoying your last year of HS and family and friends. After all, if you get your wish, you only have a bit over 8 months left at home. After that, you visit for at least the next 9 years or more.