He made an immediate impact in his first year with his new team, leading the league in passing yards and touchdowns en route to a 5–2 regular season record.

Márquez played his college football with Pumas CU in the Organización Nacional Estudiantil de Fútbol Americano (ONEFA), representing the National Autonomous University of Mexico (UNAM) from 2009 to 2013.

[2] After serving as a backup in his first season, Márquez assumed the starting role ahead of his second year after injuries to veteran quarterbacks Salvador Castañeda and José Luis Canales.

[6] He ultimately led Pumas CU to an 8–0 regular season record and an ONEFA national title (defeating Auténticos Tigres UANL in the final) on the year of the school's centennial anniversary celebrations.

[7][8] In 2011, Márquez threw four touchdowns in the Pumas' 44–24 win over Águilas Blancas IPN,[9] but they lost in the national championship game to Auténticos Tigres UANL by a score of 15–16.

[17] A week later, Márquez won his second national championship with Pumas CU by passing for two touchdowns in their 28–16 defeat of Auténticos Tigres UANL in the title game at the Estadio Gaspar Mass.

[18] He was subsequently named the Eduardo "Pocho" Herrera ONEFA Player of the Year after throwing for 29 touchdowns and only two interceptions in the regular season and playoffs combined.

[19] After his fifth and final year of eligibility, Márquez expressed that he had no interest in continuing his football career and that he would instead look for work related to his marketing degree.

[19][22] He joined Condors CDMX for the 2016 season, and threw two touchdowns in their historic 30–28 win over Mateos and his Eagles squad on opening weekend.

[29] He also set league records for longest play from scrimmage (a 94-yard pass to Enrique Barraza) and biggest comeback (27 unanswered points after a 20-point deficit).

[35] Márquez threw two touchdowns in their 21–6 defeat of Dinos Saltillo in the semifinals, winning the North Division title and a berth in Tazón México III.

[46] However, he injured his hand in the game and was replaced by Canadian import Graham Kelly as the starter in their week two matchup against league newcomers Pioneros Querétaro.

[57] At the conclusion of his final college season in 2013, Márquez again represented the Mexico national team in an American Bowl exhibition game against the United States.