Gómez began his career with Rosario Central in the youth team, joining in 2006.[4] Before starting his senior career with Rosario Central, he had a short loan spell with Sportivo Las Heras in 2013.[5] He featured for the first time for Rosario Central on 23 November 2013 during a defeat away to Olimpo.[1][6] He subsequently made sixteen appearances across the following three campaigns in all competitions.[1] On 2 February 2016, Defensa y Justicia completed the loan signing of Gómez.[1] He remained with the club for the 2016 and 2016–17 seasons, playing in twelve matches before returning to Rosario in June 2017.[1]
In January 2019, Gómez joined fellow top-flight side Argentinos Juniors on loan.[1][7] He scored his first senior goal on 18 February against Estudiantes.[1] Twelve months after arriving, in January 2020, Argentinos purchased Gómez permanently as the defender signed a three-and-a-half-year contract.[8]
At the end of January 2022, Gómez joined River Plate on a deal until the end of 2025.[9]