Baker attended Oak Ridge High School in Conroe, Texas, alongside Durbin Feltman.

[4][5][6] Baker was considered an early round prospect for the 2015 Major League Baseball draft, but emailed major league teams telling them that he would not sign and would instead attend Texas Christian University (TCU) to play college baseball for the TCU Horned Frogs.

[11] As a sophomore in 2017, Baker played 47 games before he suffered a left arm injury during a collision at first base that ended his season.

[14] The St. Louis Cardinals selected Baker in the second round, with the 75th overall pick, in the 2018 Major League Baseball draft and signed with them for $800,000.

[15][16] He made his professional debut with the Gulf Coast League Cardinals, and, after batting .500 in eight games, and was promoted to the Peoria Chiefs.

[25] In mid-September, he was promoted to the Memphis Redbirds of the Triple-A East with whom he appeared in two games to end the season.