It is that entry for Matthias, having Matthias and Sara as parents, that opened the case for the bigamy theory by the British historians.
In the case of the Puritans, baptisms did not necessarily occur directly after birth.
We also assume that he came with his parents, but nothing is mentioned in the BOOK.
Matthias Jr.'s naming choices for children could be telling:
Ebenezer? Matthias: Father Mary: Mother James: Uncle (possible) and Grandfather (possible), not to mention the King of England at the time, and the reason for their emigration. Is it possible that they were not Puritans?