[3] As a freshman at East Carolina in 2018, Burleson batted .252 with 18 RBIs over 36 games and 103 at-bats alongside pitching 54 innings, going 5–2 with a 3.33 ERA and four saves.

[14] After the season, Burleson was selected by the St. Louis Cardinals as an outfielder in the second round (70th overall) of the 2020 Major League Baseball draft.

[21][22] Burleson ended the 2021 season with a combined .270/.329/.454 slash line with 22 home runs and 76 RBIs over 119 games between the three clubs.

[26] He made his MLB debut on September 8 as the club's starting right fielder, going hitless over four at-bats with a walk in an 11–6 loss to the Washington Nationals.

[27] He collected his first MLB hit on September 11, a single off Duane Underwood Jr. of the Pittsburgh Pirates in a 4–3 St. Louis win.

[30] Burleson spent the entirety of the 2023 season with St. Louis and appeared in 107 games, batting .244 with eight home runs and 36 RBIs.