These are typical patterns, not rules.
At around 50 employees, the owner is often the plant manager. A shop foreman runs the floor, a senior machinist doubles as maintenance, a bookkeeper and an outside accountant handle the money, and IT is a managed service provider. One person raises the purchase and signs it.
At around 200, a plant manager reports to the president or GM, with shift supervisors, a scheduler, a manufacturing engineer, a quality manager and a maintenance manager reporting in. The controller usually reports to the president and checks the payback on anything big. At 1,000 or more across several sites, a VP of operations sits above the plant managers, and corporate directors for quality, EHS, IT and procurement set the standards each site buys to. A corporate program can override a site pilot, so sell to both levels.
Rough rules of thumb for a function's first dedicated owner: a quality manager around 75 to 150 employees, a controller around 100 to 200, schedulers and maintenance managers around 150 to 300, IT and EHS around 250 to 500, reliability engineers above about 400. A first hire in a new function is one of the manufacturing buying signals, because tools for it often follow.