Just the Jamestown hinterland. The Mayflower at Plymouth Rock wasn't until 1620. The English did not have a presence in the Caribbean before 1625, at St Croix. Barbados, Dominica and St Kitts were 1627.
I wonder if Maurits will have any sons or not drink himself to death at the exact age and time King James kicked it IOTL.
(I'm 30 years behind on Dutch Republic politics)