Big Leaguer (1886)

“In the evening the excursionists visited the diamond field and criticized the game between the Lynchburgs and Norfolks, and told the boys who had never seen the big leaguers how games should be played.” Alexandria Gazette, June 29, 1886, p2

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1908. “Major league teams…are frequently beaten in the spring by teams which do not class with them, because the big leaguers do not exert themselves” (The Washington Post, Apr. 1; Peter Morris)