You can begin working with this faction almost immediately after you emerge from Vault 111. Simply wander down the road from Sanctuary, heading southeast until you reach the township of Concord. Visit the Museum of Freedom. You can continue Institute operations for as long as you wish. Please be aware that unlike your relationships with the other main factions—the Brotherhood of Steel, the Railroad, and the Institute—the other plans you’re hatching tend not to affect the Minutemen negatively (unless specified). The Minutemen want to create a Commonwealth of hard-working patriots who trade and build strong bonds together.
Fallout 4 eGuide DATA The Minutemen Quests