At your first job, the person who notices the empty napkin holder becomes the person they trust.

Trust at work is built out of the jobs nobody gave you. Anyone can do what they were told; the person who spots the napkins running low, or the queue building at the other register, is showing that they are looking at the whole place rather than at their own task. Managers notice that faster than they notice talent.

Do one unassigned thing per shift without being asked. Do not announce it, and do not keep score out loud, because the point is the looking rather than the credit. Within a month you will be the one asked to train the new person.