From preliminary research that involved several sources, I learned the following about five major sports:

References to games resembling BASEBALL in the United States date back to the 18th century. Its most direct ancestors appear to be two English games: rounders (a children’s game brought to New England by the earliest colonists) and cricket.

The only major sport strictly of U.S. origin, BASKETBALL was invented by James Naismith (1861–1939) on or about December 1, 1891, at the International Young Men’s Christian Association (YMCA) Training School (now Springfield College), Springfield, Massachusetts, where Naismith was an instructor in physical education.

GOLF originated from a game played on the eastern coast of Scotland, in an area close to the royal capital of Edinburgh. … The game of golf officially became a sport when the Gentlemen Golfers of Leith formed the first club in 1744 and set up an annual competition with silverware prizes.

On December 8 1863, Association Football and Rugby Football finally split into two different organizations. Later in the year, the first ever SOCCER match was played on Barnes common at Mortlake, London on 19th December 1863 between Barnes Football Club and Richmond Football Club. The game ended in a 0-0 draw.

The modern game of TENNIS traces back to a medieval game called jeu de paume, which began in 12th century France. It was initially played with the palm of the hand, and rackets were added by 16th century.

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To obtain more information about these and other sports, I highly recommend On the Origins of Sports: The Early History and Original Rules of Everybody’s Favorite Games, co-authored by Gary Belsky and Neil Fine (2016).