The Mayflower did not establish the first settlement in New England, for George Popham founded a colony of 120 souls there in 1607, thirteen years earlier. After many died from the hazards that Captain Jones warns the Pilgrims about, the few survivors departed.
The New World was visited in 1607. In One scene they show a map of the Massachusetts area. They call it New England but they are headed to Virginia. How could they have mapped out New England without having visited it yet?
The viewer who objected to a map of New England in the possession of the Pilgrims on the Mayflower seems unaware that there was a detailed map of New England as a fold-out in Captain John Smith's "Description of New England" (1616), a book referred to by Bradford and owned by Brewster.