I have estimated the birth of Jacob Sawyer (who died ca 1827) as ca 1740 or earlier.
Jacob's son, Zephaniah, would have had to have been 21 to receive this land grant:
Tyrrell Co. DB 8
State Grant (No. 75) to Zephaniah Sawyer 1 Mar 1780 60 acres on west side of Great Aligator River & west of Frying Pan. Signed by Rd. Caswell. Wm. Sheppard D. Sec.
Therefore, Zephaniah would have been born by 1759. Jacob may not have been 21 when he fathered Zephaniah but would certainly have been born somewhere around 1740 give or take a year or two.
Frederick is mentioned first in Jacob's will so he is most likely the first born son, thus Jacob was probably born even earlier than 1740.