[4] As a sophomore in 2016, he made 15 starts, going 7–5 with a 3.30 ERA, striking out 64 batters in 95+1⁄3 innings, earning All-CCAA Second Team honors.

[9] As a senior at Cal State East Bay in 2018, he pitched in 14 games (making seven starts) while going 8–2 with a 1.94 ERA and was named to the All-CCAA First Team.

[10] After his senior season, he was selected by the Miami Marlins in the 17th round of the 2018 Major League Baseball draft.

[11][12][13] Vesia signed with Miami, making his professional debut with the Gulf Coast League Marlins before earning a promotion to the Batavia Muckdogs.

In 2018, Vesia began the year with the Clinton LumberKings before earning a promotion to the Jupiter Hammerheads in June and the Jacksonville Jumbo Shrimp in August.

[23] On February 12, 2021, the Marlins traded Vesia and Kyle Hurt to the Los Angeles Dodgers in exchange for Dylan Floro.

[27] In the 2024 NLDS, Vesia allowed only one hit in three innings, while striking out four batters,[27] however he injured an intercostal muscle in the series and was left off the roster for the NLCS.