The first 'independent colony' was the United States, as you all know.
How early can discovery of the New World and colonization of it occur?
What is the earliest possible time a colony could become independent?
How can colonization be accelerated, and at an early time?
The POD must in 1000 or 1001 at the establishment of Vinland. However you can't just have Vinland survive and lose contact, that's too easy. If your scenario involves Vinland becoming independent, then Vinland must keep contact with the Vikings before fighting for its independence some time later.
EDIT: To all Captain Obviouses: They must be in the Americas.