“Base ball caps!” (Nicely’s Emporium of Fashion advertisement). Baltimore Sun, September 28, 1865, p1
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1889. “A base-ball cap free to every purchaser” (M.J. Flavin & Co., San Francisco, advertisement for “outing suits.” Daily Evening Bulletin [San Francisco], June 10, 1889).