The name Palmer is not in his birth record
https://www.ancestry.com/sharing/21699169?h=354918&utm_campaign=bandido-webparts&utm_source=post-share-modal&utm_medium=copy-url
Going looking for parents marriage
The best I could find. No marriage to Damaris
https://www.ancestry.com/sharing/21699228?h=293078&utm_campaign=bandido-webparts&utm_source=post-share-modal&utm_medium=copy-url
Wrentham is inNorfolk not Suffolk apparently
"Massachusetts Births and Christenings, 1639-1915", database, FamilySearch(https://familysearch.org/ark:/61903/1:1:F4J9-63R : 15 January 2020), Elizabeth in entry for Thomas Force, 1693.