Somebody always notices who fills the empty shelf without being told. Usually it’s whoever writes the schedule.

Initiative is one of the few things that cannot be faked over a long period, and the people making decisions watch for it because it predicts everything else. Doing the unassigned task is not about being seen, but you are seen anyway, by exactly the person who decides who gets hours and responsibility. The noticing happens quietly and gets recorded somewhere you never see.

Find one thing in your workplace that nobody owns and start handling it. Do not announce it. Let the pattern accumulate over a few weeks before you expect anything from it.