Jay was considered one of the top prospects for the 2015 Major League Baseball draft.[6][7][8] The Minnesota Twins selected him with the sixth overall pick.[9] He officially signed with the Twins on June 17 and was assigned to the Fort Myers Miracle where he posted a 3.93 ERA in 18+1⁄3 innings pitched. The Twins transitioned Jay into a starting pitcher with Fort Myers in 2016,[10] where he posted a 5–5 record with a 2.84 ERA in 13 starts before being promoted to the Chattanooga Lookouts where he pitched to a 5.79 ERA in five games (two starts). He pitched only 11+2⁄3 innings in 2017 due to injury. Jay returned in 2018 to pitch for the Chattanooga Lookouts, compiling a 4–5 record with a 4.22 ERA in 38 games. Jay would begin the 2019 season with the Chattanooga Lookouts where he posted a 1–2 record with a 4.82 ERA in 17 appearances.[11] In 2019, he began struggling to swallow as a result of eosinophilic esophagitis and started to lose weight, which correlated with a decline in his on-field performance.[12]
Cincinnati Reds
On June 10, 2019, Jay was traded to the Cincinnati Reds in exchange for cash considerations.[13] Jay would spend the rest of the 2019 season between the Pensacola Blue Wahoos and the AZL Reds where he posted a 0–0 record with a 3.03 ERA in 18 appearances and a 0–0 record with a 9.00 ERA in two appearances respectively.[14] He did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[15] On June 1, 2020, Jay was released by the Reds.[16]
Joliet Slammers
By 2022, Jay's health problems which had correlated with his decline in performance were attributed to a diagnosis of eosinophilic esophagitis. After spending 2021 out of baseball and focusing on his health, Jay asked Joliet Slammers manager Daniel Schlereth for a tryout[12] and signed with the Frontier League team on June 7, 2022.[17] In 22 appearances for Joliet, he registered a 1.64 ERA with 24 strikeouts and eight saves in 22 innings of work. In 2023, Jay made 20 appearances (7 starts) for the Slammers, logging a 4–3 record and 4.26 ERA with 64 strikeouts and seven saves in 57 innings pitched.[18]
New York Mets
On August 24, 2023, Jay's contract was purchased by the New York Mets organization.[19] He spent the remainder of the year with the Triple–A Syracuse Mets, posting a 6.00 ERA with 8 strikeouts across 6 appearances.[20]
Jay began the 2024 season back in Syracuse, logging a scoreless appearance for the affiliate to start the year. On April 10, 2024, the Mets selected Jay's contract and promoted him to the major leagues for the first time.[21] He made his MLB debut the next day, pitching two innings against the Atlanta Braves.[22][23] In his second appearance, he recorded two scoreless innings against the Kansas City Royals. However, on April 17, Jay was designated for assignment after Michael Tonkin was claimed off waivers.[24] He was outrighted to Triple-A Syracuse two days later after going unclaimed off waivers.[25] On June 30, the Mets purchased Jay's contract, adding him back to the major league roster.[26] However, on July 2, he was optioned back to Triple–A having made just one appearance.[27] Jay was designated for assignment a second time on July 17.[28]
Milwaukee Brewers
On July 21, 2024, Jay was traded to the Milwaukee Brewers in exchange for T.J. Shook.[29]