Work.
Work everywhere. Work anywhere. Work on everything. Work on student shows. Work on "real" shows. Work on shows that you and three friends put on in the basement of a bar. (And if you don't have those sorts of friends, find them.)
The SMs who stand out aren't the ones with good grades (little secret: nobody cares what grades you got]) or even the ones who graduated from fantastic schools (the proportion of SMs with BFAs, let alone BFAs specialized in stage management, is very low compared to most professions), but the ones who have kept themselves busy. Even if you aren't working prestigious gigs, work.
Check out the attached chart, which shows the amount of resources you'll have as a stage manager over time. In high school you have relatively few; as soon as you start university, the quality and the volume will increase significantly. (At least, it will at a half-decent school.) Well-maintained facilities, new and well-maintained equipment, all sorts of experts and mentors to assist you, the first "real" show budget you'll experience, etc.
Just as importantly, your BFA resources will increase over time. As you move towards fourth year, you'll start working in more advanced venues, have more access to faculty members, be trusted to work with the newest, shiniest and most complicated equipment, and so on.
Then you graduate, and--for most students--you land pretty damn hard.
If you're a real eager beaver who positioned themselves very well (internships with prestigious companies, summerstock work, etc.), you might not have this experience: you might jump straight to apprenticing somewhere fancy and wonderful and never look back.
You might also go a route like working cruise ships or tourist shows, which will spare you the worst of this phenomenon.
But if you're like most BFA students, after you graduate, you leave this land of milk and honey (state-of-the-art facilities and equipment, amazing instructors, decently-sized budgets...), and find yourself pulling together shows in church basements with no resources and a budget of "How many coins can we pull out of the director's couch."
It's possible to claw yourself out of there. But it's easier if you have practice, and it's easier if you have the sort of experience needed to hook yourself into more prestigious and better-paying gigs. You get both that practice and that experience by doing it while you're still a student, and this will spare you the hardest, lowest and most difficult part of that trough.
Conversely, if your entire work background consists of your one annual show in the mainspace with only the finest equipment and personnel, and now you suddenly have to dye costumes in your parents' bathtub and your "venue" is a disused massage parlor in a dingy strip mall and--indignity of indignities--they expect you (YOU! The Stage Manager!) to fold the programmes by hand, that's when you have a nervous breakdown and leave the profession at age 25.
But, at bare minimum, if you reach that stage of your career with zero experience or expertise in handling these situations, it's going to be harder, it's going to take longer, and you're more likely to fail. Get the practice now, when the stakes are fairly low and the benefits are fairly high, and you'll thank yourself later.