He attended Toledo Mud Hens games at Fifth Third Field as a child, but moved to Florida for high school.
[4] In four seasons with the Toronto organization, Winckowski made 54 appearances (50 starts), compiling an 18–17 win–loss record with a 3.35 earned run average (ERA).
[4] On January 27, 2021, Winckowski was traded to the New York Mets alongside Yennsy Díaz and Sean Reid-Foley in exchange for Steven Matz.
[13] Winckowski was next recalled for a start on June 15,[14] and registered his first MLB win after pitching five scoreless innings in a 10–1 victory over the Oakland Athletics at Fenway.
[21] For the 2023 season, Winckowski appeared in 60 Red Sox games (one start) and posted a 4–4 record with three saves and a 2.88 ERA while striking out 82 batters in 84+1⁄3 innings.