I wouldn't count on getting any range time unless you make it happen yourself. It just isn't a priority for medical commands. Hell, I just deployed with a Marine unit and when our predeployment workup schedule got compressed, the first thing they dropped was the M9 familiarization fire.
But many bases have public access ranges that offer the qualification courses for pistol and rifle (rifle is often a reduced distance with scaled down targets) weekly or monthly. Pay your $25 or $30, shoot, get the paperwork.
Anyone in the Navy who wants to shoot more often and more seriously (and get the pistol and rifle qualifications + ribbons ... or even the leg/Distinguished medals) can show up to either the Atlantic Fleet or Pacific Fleet matches (held at Quantico and Pendleton respectively), and get a few days of really great instruction with a pistol and rifle. Bring your own weapons, or use loaners provided by the team. Free ammo. Free lodging (open bay barracks if you can tolerate it, I can't) or stay in the BOQ or whatever hotel you want. Some commands will provide funded TAD orders but most people end up with no-cost TAD orders. Everyone's welcome, including complete beginners. Marines, Army, and a bunch of civilians come to the Atlantic matches too. It's a great time ... usually about 9 or 10 days of shooting.
Most years they're held in April or early May but due to COVID-19 the Atlantic event has been rescheduled for August, and the Pacific event will be in September.
In non-COVID-19 years, the top 20 from the year's east/west combined All-Navy matches are the "team" (prior year team members and those with points toward Distinguished are also welcome). This is the group that represents the Navy at Interservice and Nationals ... but actually anyone in the Navy can show up to those matches and be part of the group ... only expectation is that they keep up and not get in the way, as these aren't really "learning" events.
The Army has a formal marksmanship unit full of people whose full-time job is to practice and travel for competition. I think I can count on my fingers the number of Air Force people I've seen at Interservice or Nationals over the years. I'm sure some show up, but I don't think they have a real organized team. Navy definitely has the best opportunities for people whose jobs aren't primarily trigger pulling to walk on and be part of it.
Navy Info -
Best kept secret in the Navy.