AZL General Discussion, page-5885

I think you have your sequence of events a little mixed up champ..

Baseball Origin:
Baseball likely had its origins in the early 1800s, possibly as a mash-up of a variety of different stick and ball games that had been around for centuries. These proto-baseball games included England’s cricket or rounders and even games played in ancient Egypt, by Mayan tribes, or in France, although the England story is the most plausible.

Cricket Origin:
Village cricket had developed by the middle of the 17th century and the first English “county teams” were formed in the second half of the century, as “local experts” from village cricket were employed as the earliest professionals. The first known game in which the teams use county names is in 1709.