Braxton was drafted by the Braves in the 1st round in the 2014 draft out of high school in Asheville, North Carolina. His draft season was spent in left field, and he split time between the Braves GCL team and the advanced rookie Danville team. Altogether, he hit .224/.387/.299 with a 31/42 BB/K ratio. He did not hit any home runs, but he showed excellent power in his swing as well as his patience at the plate.
The Braves pushed Davidson to full-season A-ball Rome in the South Atlantic League for 2015. He spent the entire season in Rome, playing right field.