And it's not just ship crews, which could be anywhere from 50 to 1000. There's also starbase/outpost personnel, land-based facility people, maintenance crews, auxiliary services, recruiting offices, etc., multiplied by the hundreds of planets in the Federation. The total number of people could be well over a million.
Eh, China alone has 3 million people total in all branches of their armed forces. The US over 2 million.
You have hundreds of worlds with millions and billions of people each I expect Starfleet would easily have billion's of personnel.