For once, I agree with the FamilySearch Family Tree. There are no known primary sources showing the birthplace or parents of this Nicholas Knapp. Wells-Next-Sea, Wells, Norfolk, England, is almost certainly incorrect, since, according to a note on his FamilySearch profile, the Nicholas Knapp who was born there was christened 16 Mary 1592, and all his children were born in England; this Nicholas Knapp was probably born closer to 1606, based on the birth of first child in 1631 (according to "The Great Migration"). "The Great Migration" also states that his origin is unknown.
I think the theory that his birthplace was Bures St Mary [Parish], Suffolk, England, came from a William Knopp (note the different surname) being from there, and some people thought they were brothers, despite their 25-year age difference, but as "The Great Migration" also points out, there is no evidence of a Nicholas Knapp in Bures St Mary.
The birth info for this Nicholas Knapp should probably be changed to born between 1606-1612 in England, based on the birth of first child Jonathan in Nov 1631, according to "The Great Migration."