Albert Almora made his first appearance at Cooperstown Dreams Park with the Broward Bulldogs (FL) during week 2 in 2005. He returned twice in 2006, week 5 with the Miami River Dogs (FL) and N.A.T.C. with Team Rawlings Black (MO). With the Miami River Dogs, Albert was crowned the King of Swat hitting six homeruns.

Albert attended and graduated from Mater Academy Charter High (Hialeah Gardens, FL) where he played on the varsity baseball team since 8th grade. During his freshman season (2009), Albert posted a .423 BA, with 34 RBI, 13 doubles, 6 triples and 3 home runs. Albert’s accolades include Baseball Coaches Association (BCA) Rookie of the Year Award, freshman of the year and ranked number one in the world as a 14-year old by USA Baseball (2009).

In addition to his scholastic team, Albert played on six national teams, tying a record. He competed with the 2009 16U USA National team in Taipe, Taiwan. The team won gold against Cuba. In 11 games, Albert's stats included .356 BA (15 RBI, 3 doubles, 1 triple and a home run), 5 stolen bases and walked 3 times. A member of the 2010 18U USA National team, the squad finished the summer with 19-2 record and tournament-best 7-1 in the World Championships. He was named USA Baseball's athlete of the year in 2011 after leading the 18 and under team to a 9–0 record, was named the tournament MVP, and won the USA Baseball Richard W. “Dick” Case Player of the Year Award.

The outfielder made the leap to professional baseball when the Chicago Cubs selected him sixth overall in the 2012 Major League Baseball draft. Albert made his professional debut on June 8, 2016. He went on to win the World Series with the Cubs the same year.