In the background section it says "Founded in 2180 by ordinary folk…"
And in behind the scenes is mentioned, they "as a whole come[s] from the legacy of the Minutemen.
I yet have no exact idea, how to, but those two sections have to be connected. Scrolling the Wikipedia article further down, to Legacy, you find the same statue, that in-game is placed before the bridge to Sanctuary Hills, in the real world in Concord. Also Preston Garvey holds for a moment there (on their way from the Museum of Freedom) and notes: "Well I'll be damned. It's the monument to the original Minutemen. I knew that was somewhere around Concord. That means this right here must be the Old North Bridge. Where the first shots of the American Revolution were fired."
By the way, Fallout 4's Minutemen are mentioned in that Wikipedia article there. ;o)
So, to me it appears as if this article has to be expanded. Though I don't have much – if any – experience in connecting real world history and game lore, thus "no exact idea". -- -- You like to talk to me? -- cCContributions -- 10:19, 10 January 2017 (UTC)