If you haven’t yet read every page, dropdown and link at USNA.edu, I recommend it. Many answers are there.
Soccer at USNA for both men and women is Div I, Patriot League, and actively recruit for their sports according to NCAA rules. You can drop deeper into schedule and press releases at navysports.com
During plebe summer, there are walk-on tryouts for the varsity sports. If your caliber of play is at this level, then a window of possibility is open.
Midshipmen typically participate at either varsity, club or intramural level, depending on their talent, interest and time available. Varsity players typically put a lot of time into their sport, intramurals, proportionately less so. There are plenty of briefs about everything.