Born and raised in Greenfield, Indiana, Jameson played two years of college baseball at Ball State University.
[4] As a sophomore in 2019, he started 16 games and pitched to a 6–3 record with a 3.24 ERA and 146 strikeouts over 91+2⁄3 innings and was named the MAC Pitcher of the Year.
[5] The Arizona Diamondbacks selected Jameson in the first round, with the 34th overall pick, of the 2019 Major League Baseball draft.
[6][7] He signed for $1.4 million and was assigned to the Hillsboro Hops of the Class A-Short Season Northwest League.
[12] After starting 12 games and pitching to a 2–4 record with a 3.92 ERA and 77 strikeouts over 64+1⁄3 innings, he was promoted to the Amarillo Sod Poodles of the Double-A Central in late July.