“Mayor Shepherd has promised to make the opening address and throw out the first ball.” St. Joseph (MO) Daily Herald, April 28, 1895, p3
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1908. “There were many prominent spectators in the stands, which were overflowing long before Commissioner Morrow threw out the first ball” (The Washington Post, Apr. 28; Peter Morris).