Staff is a mass noun; it refers to a (uncountable) group. Prefixing it with the indefinite article still indicates a group, though now the group is unspecified (i.e. indefinite).
In other words, the only time a native English speaker would use "a staff" (when not talking about some kind of walking stick) is in the sense:
Mary hired a staff to handle the wedding, including an event planner, a cook, a photographer, and some ushers.¹
A kitchen staff usually comprises a head chef, a saucier (or sous chef), a few line cooks, and a dishwasher
Using "a staff" to mean "one of the staff" would be received as awkward and confusing (and a bit dehumanizing, and hence demeaning, to the staff member in question; which means you could use it sardonically in precisely that sense).
¹ Though this is perhaps a bad example, because makes it sound like she hired each of those individuals separately; that's certainly possible, but to hire "a staff" carries the connotation that she hired them as a group, that came together (perhaps from a specialized wedding supplier).