Your professors and your university want you to succeed. They want you to get a job or go to grad school, and be out in 4 years. All those things reflect favorably on them. Big class or small class, your professors (and TAs) will be paying attention. Any competition is most likely going to be coming from within yourself, not externally.
Ultimately you can blow off the work but as you are already experiencing, it will be noted. Remember at some point too you’ll be needing profs to write LORs. You want to be making a good impressions.
Love the idea of seeing if there is any kind of mentor program to connect you with an upperclassman.