Fishman was drafted in the 30th round by the Toronto Blue Jays in 2016 and worked his way up to Double-A New Hampshire in 2019. After the 2020 minor-league season was canceled because of COVID, he was selected by the Miami Marlins in the first round of the Rule 5 Draft. He was 5-1 with a 3.67 ERA for Triple-A Jacksonville in 2021. After posting a 4-0 record and 1.87 ERA in 43 1/3 innings of relief at Jacksonville in 2022, Fishman was called up by Miami on July 29 and made his major-league debut two days later against the New York Mets. Jake pitched for Team Israel in the 2017 World Baseball Classic in South Korea and in the 2020 Olympics.