Arrive by 1640. As of 2014 his origins and parents are still unknown. As Anderson points out often simply finding a baptism record in England of a per with the same name does not demonstrate they are identical to a New England immigrant. Additional evidence is reqired.
Page Surname Listing from George Page: John Page bp 1 May 1614 in Worlington, Suffolk, England to Thomas and Cisley Page. Note this has not been proven to be the same person as the New England Immigrant