 While attended St. Ladislaus High School in Hamtramck, Gromek considered becoming a priest, but decided on a career in baseball instead, playing sandlot baseball in the area, as the school did not have a baseball team.Shortly after graduating, Gromek signed with the Cleveland Indians as an infielder after being discovered by Indians scout Bill Bradley.In his first professional season, Gromek batted .283 with two home runs as a second baseman for the Mansfield Braves and Logan Indians.