In total, Báez recorded 52 RBIs in 30 games. During his time at ACD, he never played a position steadily. After working at second base, Báez was moved to shortstop once the team lost a player. Besides these positions, he also played as a center fielder and as a catcher. He committed to play college baseball at Jacksonville University. The Chicago Cubs, led by Jim Hendry, selected Báez in the first round, with the ninth overall selection, of the 2011 Major League Baseball draft. He began his professional career by playing shortstop for the Arizona Cubs of the Rookie-level Arizona League, where he only played in three games, recording three hits, including two doubles, in 12 at-bats and two stolen bases. Promoted to the Boise Hawks of the Class A-Short Season Northwest League, Báez recorded one single in six at bats across two games. On September 29, 2011, he was selected third overall by the Leones de Ponce in the Liga de Béisbol Profesional Roberto Clemente's (LBPRC) rookie draft, but did not play due to the Cubs' limitations. Before the 2012 season, MLB.com rated Báez as the 62nd best prospect in baseball. He remained with the Cubs in extended spring training with other prospects, participating in 26 games and hitting 6 doubles, 3 triples, and 8 home runs, with 28 RBI, 11 stolen bases, and 23 strikeouts in 94 plate appearances. He made his regular season debut with the Peoria Chiefs of the Class A Midwest League. He was promoted to the Daytona Cubs of the Class A-Advanced Florida State League (FSL). "Baseball America" included Báez in two of its "Best Tools" lists, naming him the "Most Exciting Player in the Midwest League" and the "Best Defensive Infielder" in the Chicago Cubs system. Before the 2013 season, MLB.com rated Báez as the 16th best prospect in baseball. The Cubs invited him to join their major league team in spring training, competing in the Cactus League. Báez hit four home runs in five at-bats over the course of two games, including in an unofficial exhibition game against the Japanese national baseball team that was preparing for the 2013 World Baseball Classic. He concluded spring training with a .298 batting average and 10 RBIs. Báez returned to the Daytona Cubs to open the 2013 season. On June 10, 2013, Báez hit four home runs in one game, becoming the second player to do so in the history of the FSL.