Most of the Biographical Dictionaries and Encyclopedias are agreed that he was born on 2nd January 1647 at Friston Hall in Suffolk to Thomas Bacon Esquire and Elizabeth (nee Brooke) Bacon, but I have not been able to find a baptism register entry for Nathaniel. The Suffolk parish registers are not online yet, although Ancestry is currently digitising and indexing them, so hopefully once that project is complete I will be able to confirm this.