After graduating from Rancho Bernardo High School,[1][2] Williams played college baseball at Arizona State University for the Sun Devils from 2011 to 2013.

[7][8] He made his professional debut with the Gulf Coast Marlins and also played for the Batavia Muckdogs and Greensboro Grasshoppers that year.

Williams started 2014 with the Jupiter Hammerheads, earning Florida State League All-Star honors, and was promoted to the Jacksonville Suns in August.

In 2015, Williams played for both Jacksonville and the New Orleans Zephyrs, pitching to a 7–10 record and 3.85 ERA in 25 games (24 starts).

Williams posted a career year, finishing with an ERA of 3.11 in 31 starts, ending the season with a record of 14–10 in 170+2⁄3 innings.

[23] On July 30, 2021, Williams was traded to the New York Mets along with Javier Baez and cash considerations in exchange for Pete Crow-Armstrong.

On July 14, 2022, Williams recorded his first career save after tossing three scoreless innings of relief against the Chicago Cubs.

[28] Williams is a devout Catholic; he is a member of the Knights of Columbus and his heavily-tattooed arms include the initialized motto of the Society of Jesus, "AMDG," and an allusion to Benedict of Nursia.