If you find a chemistry set at a school, you can disassemble it to get several glass flasks, IIRC.
I don’t think there’s any grand design regarding yeast production.
Lab access isn’t meant for mid or late game only. You can access and survive labs quite early, assuming you don’t have a particularly weak (or weakened) character, and assuming it’s not an ice lab. By running and closing doors you can avoid a lot of combat. The entrance turret is not a threat if you know ways to deal with it.
Edit: Oh wait… you have 25 spawn rate. But does that actually affect lab spawns?