While some Vault-Tec Workshop content becomes available the moment you take control of your first settlement, it takes a bit of work to unlock everything this DLC has to offer.
The first Vault-Tec quest is automatically added to your Pip-Boy’s quest log when you reach Level 20. You can also begin this quest by visiting Quincy Quarries (located west of Quincy Ruins, near the Commonwealth’s southeast corner). From that point on, it’s simply a matter of progressing through the Vault-Tec quest line. Related rewards include new buildable items, a legendary Vault jumpsuit, and control of a massive underground settlement.