If you count professional baseball history (and not just the majors), the earliest confirmed unassisted triple play was by a first baseman. And that first baseman later was the head coach of the 1906 Rutgers Baseball Team.
March 14, 1906 Daily Home News of New Brunswick:
"Announcement has been made that Rutgers has secured Harry O’Hagen, the crack baseball star, of Newark, to coach the baseball nine this season. Mr. O’Hagen is well known in the baseball world, having played for several years on the New York Nationals, as first base and last season in the same capacity on the Newarks, of the Eastern League. He will come here shortly and begin his work, which will last only through the month of April. With a man like O’Hagen to coach, Rutgers ought to get a good team on the diamond this season that will do credit to the college.”
"July 15, 1902: Harry O’Hagan of the New York Giants recorded the third out of a 1*-4*-3* triple play turned against Cincinnati. O’Hagan subsequently was sent to the minors (Rochester, Eastern League) and he turned an
unassisted triple play as a first baseman a month later (8/18/1902) against Jersey City."
"Monday, August 18, 1902:” First baseman Harry (Hal) O'Hagen of the International League's Rochester Bronchos executed the first authenticated unassisted triple play in organized baseball against the Jersey City Giants. A 10-year veteran of Major League Baseball, O'Hagan had just accepted the position of player/manager of the Bronchos, replacing Ed McLeon. He caught up with his new team on the road in Jersey City, where he promptly made baseball history.
Early in the game, with two on and none out, O'Hagan snagged a bunt out of the air off the bat of Johnnie Butler and scrambled to first base to double up Mack Dooley. George Shoch, who had been on second, never realized the ball was caught and was racing around third towards home plate. O'Hagan ran over to second base and stepped on the bag to end the inning, helping Rochester to a 10-6 victory. O'Hagan's feat is still recognized by many historians as the first unassisted triple play in professional baseball."