Conine attended El Modena High School in Orange, California, where he played three years of varsity baseball.
In 2016, Conine's freshman year, he made 15 appearances (three starts) in which he went 3–3 with a 5.10 ERA, striking out 24 batters over thirty innings.
[7] Conine signed with the Astros and made his professional debut that year with the Tri-City ValleyCats of the Low–A New York–Penn League, going 1–1 with a 1.99 ERA over 31+2⁄3 innings.
[10][11] After 15 games with Fayetteville, he was promoted to the Corpus Christi Hooks of the Double–A Texas League in August, with whom he finished the year.
[20] On February 28, 2024, Conine signed with the Lake Country DockHounds of the American Association of Professional Baseball.