The professional Lacrosse league called Major League Lacrosse was founded in 1999 and had its first season in 2001. Plus are you talking about women or men?
Although the definition of "major league" has been argued, present day MLB, as well as the Hall of Fame, define the first "major" league as the National League founded in 1876. The link below describes the first game played in that league, on April 22, and mentions that Jim O'Rourke got the first hit in that game.
The American League grew out of the minor league Western League (founded 1893) which renamed itself the American League in October 1899. The league declared itself a major league on January 28, 1901, and played its first major league season that year.
The MLS or Major League Soccer currently has 19 teams in its league. Three of those teams are Canadian. Toronto was the first to join in 2006 making that the year the MLS was founded.
Professional baseball in the USA has a continuous history from 1876, when the National League was founded, until today. A National Association existed from 1871 to 1875, but there is controversy on whether this was an actual league or not.
The National League began in 1876 and the American League started in 1901. The Cincinnati Reds were the first professional team founded in 1869 and were known as the Red Stockings back then.
The Detroit Tigers were founded in 1894. They played their first game as a Major League team on April 25, 1901.
The first major league of baseball (National Association) was founded in 1871. The National Association disbanded in 1875 and the National League began in 1876. The American League became a major league in baseball in 1901. The first World Series was played in 1903. College football became big with many universities beginning programs. The first bowl game (Rose Bowl) was played. The National Football League, then known as the American Professional Football Association, was founded in 1920. Basketball and volleyball were invented.
Tom Wills is recognized as the founder of the game of "Aussie Rules Football" back in the 1850's and 1860's. He was not the founder, however, of the AFL, which was founded, as such, in 1990. The Victorian Football League was the first major league founded in Australia for playing the game, in 1896.
The first major league in baseball was the National Association (NA) which was founded in 1871. Controversy exists over whether the National Association was a "major league." In 1968, Major League Baseball (MLB) founded a "Special Baseball Records Committee" specifically to rule on these matters, and decided that records from the National Association would NOT count in "major league" record totals. Thus, if Joe Schmoe got 100 hits in 1875 while playing in the NA, and 150 hits in 1876 while playing for a National League (NL) team, his official total number of hits in MLB competition would be recorded as 150, not 250. Whether that is what SHOULD have been decided is still argued today. The first NA game was on 1871 May 4. The first NL game was on 1876 April 22.
Saves has been a statistic since the first major league (National Association) was founded in 1871. In 1871, Harry Wright of the Boston Red Stockings led the league with 3 saves.
The American League began as a minor league called the Western League whose first season was 1894. The named was changed to American League for the 1900 season and the AL declared itself a major league for the 1901 season.