Doing one thing nobody assigned you will get you noticed faster than doing ten things they did.

Assigned work shows you can follow instructions, which is also what everyone around you is doing. Work nobody asked for shows judgement, because you had to notice the gap yourself and decide it was worth your time. That part cannot really be taught, which is why one unrequested fix gets remembered while ten completed tasks blur into each other.

Find one problem nobody has claimed and fix it this week. The messy shelf, the missing instructions, the thing everybody complains about. Keep it small enough to finish without needing permission.