Odom was the Atlanta Braves 13th round selection in 2013 out of Huntingdon College in Alabama. In his draft season, Odom split his time nearly even between the GCL and Danville. Combined, he hit .216/.310/.257 with a 10/23 BB/K ratio over 87 plate appearances, but he flashed high end defensive ability in spite of a low caught stealing percentage (9% on the year combined between the levels on 22 attempts).
The Braves skipped Odom over low-A Rome to high-A Lynchburg in 2014, and he flashed his power bat and defensive skills, but the bat stayed stagnant with the jump in levels, as he hit .