To unlock Machinist you just need access to the city of Ishgard, which you get right at the start of the HW MSQ. No other classes or jobs required (needing secondary classes leveled to unlock jobs used to be a thing but was removed in SB.)

All expansion jobs start at higher levels. The HW jobs (MCH, AST, DRK) start at level 30, the SB jobs (RDM, SAM) at level 50, and the ShB jobs (DNC, GNB) at level 60.