The New York Mets selected Orze in the fifth round, with the 150th overall pick, of the 2020 Major League Baseball draft.[3] He did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[4] Orze made his professional debut in 2021 with the High–A Brooklyn Cyclones and was promoted to the Double–A Binghamton Rumble Ponies and Triple–A Syracuse Mets during the season.[5] Over 34 relief appearances between the three teams, Orze went 4–2 with a 3.08 ERA and 67 strikeouts over 49+2⁄3 innings.[6]
Orze spent the majority of 2022 with Syracuse, also making two scoreless appearances for the Single–A St. Lucie Mets. In 32 appearances out of the bullpen for Syracuse, he recorded a 5.13 ERA with 64 strikeouts across 47+1⁄3 innings pitched.[7] Orze returned to Syracuse in 2023, making 39 appearances and posting a 3–4 record and 5.31 ERA with 81 strikeouts over 61 innings.[8]
Orze began the 2024 campaign with Syracuse, compiling a 3.76 ERA with 56 strikeouts and two saves across 38+1⁄3 innings pitched. On July 6, 2024, Orze was selected to the 40-man roster and promoted to the major leagues for the first time.[9] He made two appearances during his rookie campaign, striking out one batters across 1+2⁄3 innings pitched.
