Okey attended Eustis High School in Eustis, Florida. Playing for the school's baseball team, Okey was a four-year letterman. He also played for the United States national youth baseball team. In his senior year, Okey had a .411 batting average with four home runs and 29 runs batted in (RBIs). The San Diego Padres selected Okey in the 31st round of the 2013 Major League Baseball draft, but he did not sign.
Okey enrolled at Clemson University in order to play college baseball for the Clemson Tigers. He split time during his freshman year between catcher and designated hitter. As a freshman, Okey batted .248 with four home runs, and 41 RBIs in 61 games played. In 2015, his sophomore year, Okey started at catcher in all of the Tigers' 61 games, and had a .315 batting average and led the team with 12 home runs and 57 RBIs. He was named to the All-Atlantic Coast Conference team, an All-American, and a semifinalist for the Johnny Bench Award. In 2016, Baseball America rated Okey as the 25th-best college prospect available in the 2016 Major League Baseball draft. He was named a Preseason All-American before the 2016 season.
The Cincinnati Reds selected Okey in the second round, with the 43rd overall selection, of the 2016 draft. Okey signed with the Reds, receiving a reported $2 million signing bonus, and made his professional debut with the Billings Mustangs of the Rookie-level Pioneer League. After playing in nine games for Billings, he was promoted to the Dayton Dragons of the Class A Midwest League. Okey finished the 2016 season with a .227 batting average, six home runs and 22 RBIs. Okey spent the 2017 season with the Daytona Tortugas of the Class A-Advanced Florida State League, posting a .185 batting average with three home runs, 28 RBIs, and a .514 OPS.