Starting puppy classes before having all of her shots?

Hi all! My husband and I recently brought home my first adult dog this month, she's an 11 week old standard poodle. I've been kind of anxious about socializing her, but with her not having all of her shots I feel like we're pretty limited on what we can do. We've been sitting in our front yard with her so she can watch people, cars, and other animals during the day, and we've been trying to take her to PetSmart and other dog friendly places without letting her walk on the ground.

I've been thinking about trying to get into one of the STAR puppy classes in my area, and so far the ones I've spoken to haven't had any issue with her not having all of her vaccines but I'm still a little iffy on it. I really don't want her to get sick, but I also really want her to be well socialized. I'm worried that we're not doing enough to socialize her right now, and if we wait to do the puppy classes it'll be too late. Any advice would be greatly appreciated!!