Also hoping to make the cross country & track teams. I was told during Plebe Summer there's times where anyone interested in XC is able to run & that there's tryouts at some point over summer. I also remember hearing somewhere that it's a very much you-cut-yourself kind of program. If anyone has more info. I'd love to hear it/ask questions
The coach does not have plebes run during PS. The (mostly) recruited kids meet during sports periods but they don't run until summer is over. And that's usually when there is an opportunity to try out as well, but I'd encourage plebes to reach out sooner. The varsity usually spends first 2 weeks of August training in some location other than Annapolis, like New Mexico or Colorado, for example.
There is a plebe track smoker towards the end of July in which plebes(track recruits and others), compete for fun and company bonding time. Coaches are usually present.
As far as times, as a previous poster suggested, look around in this forum or at Navy track/xc pages for meet results to give you an idea. Off the top of my head though I'd say 5k's under the 16 minute mark and mile times under 4:25 would probably be a good start to get the coaches attention.
And finally, XC and Track are 4 season sports in terms of training. They can be a massive time suck and are a big commitment.