American Colonies included?
Savage's Dictionary of the First Settlers of New England, A-C, lists two men:
Bay, or Bayes,
Matthew, Ipswich 1659.
Thomas, Dedham, by wife Ann had Ruth, born 2, baptized 16 July 1643; and Thomas, 1, baptized 22 March 1646; removed to Boston
which means there was a man named Matthew Bay/Bayes in Ipswich, Massachusetts, by 1659. And a Thomas Bay/Bayes was in Dedham, Massachusetts, and had two children by his wife Ann born and baptized there, and then he moved to Boston, Massachusetts.
I assume that Savage's abbreviations mean that Thomas' daughter was born 2 July 1643 and Thomas was born 1 March 1646, but I am not positive about that part.
the book is out of copyright, free and digitized at
https://archive.org/details/agenealogicaldi00unkngoog/page/n6Look for the Great Migration series also. That won't be online however, at least not free. Maybe at americanAncestors.org. Every so often they offer free access to databases, so keep an eye out.
Savage's book is dated 1860 and more recent research might have found more men. In fact, I think there might be an update to Savage's book itself. He did A - Z by the way, but I guess when they digitized it they broke it up in pieces.