When he was three years old his parents, Hiram Burgos Delgado and Ivette Irizarry Arce, introduced him to the sport by visiting baseball parks.

Burgos expected to be selected in the 2008 Major League Baseball draft after recording a 9–1 season while pitching for Bethune-Cookman University, but was disappointed after going undrafted.

[4] Burgos spent the 2016 campaign with the Triple–A Colorado Springs SkySox, compiling a 10–10 record and 4.40 ERA with 115 strikeouts across 27 games (25 starts).

[5] On December 15, 2016, Burgos signed another minor league contract with the Brewers that included an invitation to spring training.

[7] He made 18 appearances (15 starts) split between Biloxi and Colorado Springs, posting an aggregate 4–5 record and 6.06 ERA with 64 strikeouts across 62+1⁄3 innings pitched.