The New York Mets selected him in the ninth round, 260th overall, of the 2018 Major League Baseball draft.[7] He signed with the Mets, beginning his professional career. Montes de Oca underwent multiple surgeries after being drafted, however, and made his professional debut on May 5, 2021, with the High-A Brooklyn Cyclones.[13] He finished the year with the Double-A Binghamton Rumble Ponies, posting a 4.50 ERA with 47 strikeouts and 6 saves in 34.0 innings of work across 28 games for both teams. He began the 2022 season with Binghamton before being promoted to the Triple-A Syracuse Mets. In 44 combined games, he registered a 3–3 record and 3.33 ERA with 80 strikeouts and 11 saves in 51.1 innings pitched.[14]
On September 3, 2022, Montes de Oca was selected to the 40-man roster and promoted to the major leagues for the first time.[15] He made his MLB debut the same day, striking out one batter and yielding one hit, one walk and no runs pitching 2⁄3 of an inning to finish a 7–1 loss to the Washington Nationals.[16] He finished his rookie campaign with a 10.80 ERA and 6 strikeouts in 3.1 innings across 3 appearances.
On March 28, 2023, it was announced that Montes de Oca would undergo arthroscopic surgery to remove bone fragments from his right elbow, sidelining him for four months.[17] During the surgery, doctors discovered that he needed Tommy John surgery and performed the procedure, ending his 2023 season.[18] Following the season on November 2, Montes de Oca was removed from the 40–man roster and sent outright to Triple–A Syracuse.[19]