His father was born in Beirut, Lebanon, and played soccer in his native country before moving to the United States at the age of 15.

[5][6] Considered one of the top prospects for the 2017 Major League Baseball draft,[7][8] the Pittsburgh Pirates selected him with the 12th overall pick.

[11] Baz spent 2017 with the Gulf Coast League Pirates, posting an 0–3 record with a 3.80 ERA in 23+2⁄3 innings pitched.

[17] Baz began the 2019 season in extended spring training before reporting to the Bowling Green Hot Rods in early May.

[23] He made his post-season starting debut in the second game of the American League Division Series against the Boston Red Sox on October 8, 2021.

[24] On April 16, 2022, Baz was placed on the 60-day injured list as he continued his recovery from arthroscopic elbow surgery, which he underwent in late March.

[29] On July 2, 2021, Baz was named to the roster for the United States national baseball team for the 2020 Summer Olympics, held in 2021 in Tokyo.