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FYS"Yes, Joann, here is the outline of that episode from Burns' work onbaseball:
Inning One, "Our Game", looks at the origins of baseball in the 1840s and takes the story up to 1900. Burns refutes the myth that Abner Doubleday invented baseball in Cooperstown and traces its roots instead to the earliest days of the nation — there are records of a game called "Base" played at Valley Forge. (This is where they show the book and mention it)"
Rounders is a children's game in England. That was certinaly played well before Mr. Doubleday. Baseball, a combination of cricket and rounders, can be argued when it truly started. It certainly was played before Cooperstown, but that gets into the official introduction vs. unofficial playing.
So Cooperstown is likely the birthplace of organized baseball. The true origin is up for debate, but probably goes back to the 1600's.