That’s about how we started - similar size, no machine shop or practice area. We ended up working out of a parent’s garage and basement that year.
Since your school doesn’t have what you feel you need to help grow your team to the next level, I suggest you look out in your community. We managed to form a partnership with a local engineering co-op that had a full machine shop for our second and third years. The owner of the building rented us space for the build season (and a big closet to store all our stuff during the off season) real cheap, and we had full run of the machine shop in the evenings/weekends.
That was such a productive relationship, the school decided to get a 3 year lease on a space in the building for us, and completely redid it to meet our specs for what the team needed. We’ve managed over the years to accumulate a fairly impressive set of machines and tools, mostly by looking out for great deals in the area, local auctions, and craislist.
I know it can look bleak when you see what 10+ year old teams have available and compare it to what you have just starting out. But keep your eyes on the end goal, set up a list of things you want, and be aggressive about getting what the team needs!