You know to take this idea further, why not like, 18-20 year old characters instead of 20-25 even?
I guess because of the rigors of military combat or something? Is the physical body not strong enough then or something?
A lot of the privates would be in that age range or close to it. I left for basic training about a month and a half after my 18th birthday, and while there were some recruits who were older ( even a couple in their 30s), the majority were not long out of high school. I was 20 or 21 when I made Corporal, which is the first NCO (manager, roughly in civilian speak) rank. That was also fairly typical, with most Corporals or Sergeants being early to mid twenties. To give an idea of how young most people are, we had a guy in my platoon whose nickname was Old Man. He was maybe 32 years old when he was a Corporal.
Young adults in a fictional military organization aren't unrealistic...they should be common! The key though is that they're all people who've been in the military for four years or less, and so aren't in very senior positions. It takes a lot of time and experience to climb the organizational ladder, just like the corporate hierarchy in a typical civilian office. The most senior role that young enlisted personnel might be in would be fire team or squad / section leader (Corporals and Sergeants) and young officers (Lieutenants) commanding platoons.
An enlisted person may reach Corporal by the end of four year term of enlistment, and maybe (rare!) Sergeant. Gunnery Sergeant, which is the equivalent of ME's Gunnery Chief, is going to be out of range until probably the third term (8+ years in). Officers may reach Captain (ME's Staff Lieutenant I believe) by the end of four years in, but Major (ME's LCDR) is closer to 10.
Tl;dr: A young adult character is plausible if they're junior enlisted or a lieutenant not long from college and officer candidate school, but not as the ship's commanding officer or the platoon sergeant. Those two roles should be filled by more senior officers and NCOs, who in order to be plausible, probably should have been in the service for several years. Late 20s or 30s are better age ranges for characters with those roles as their background.