González began in Mexican open-wheel competition in 1995 with a Formula 3 Mexico entry, followed by a single Indy Lights Panamericana start in 1998. In 2001 he entered the Formula Chrysler Euroseries, winning twice and finishing second in the championship. He moved to the World Series by Nissan in 2002 with GD Racing but went pointless across seventeen starts.
González made his Champ Car debut in 2003 at St. Petersburg for Dale Coyne Racing but failed to finish. He appeared again that season at Mexico City, substituting for Roberto Moreno with Herdez Competition, taking tenth place and his first Champ Car points. A full-time ride at PKV Racing followed in 2004 with backing from the Mexican arm of Nextel. He contested fourteen races, recording a best finish of seventh at Cleveland, and ended the season fifteenth in the standings. He was not retained for 2005.
After a hiatus from top-level competition, González returned in 2012, making three starts with RSR Racing in the American Le Mans Series and one in the FIA World Endurance Championship with Greaves Motorsport. He appeared with the Manor team in the 2016 WEC in two rounds and remained with the team's successor CEFC Manor TRS Racing for the full 2017 season, finishing eighteenth in the championship. His Le Mans debut came in 2017 with CEFC Manor alongside Vitaly Petrov and Simon Trummer; the car retired after 152 laps.
In the 2018–19 WEC superseason González drove for DragonSpeed. He finished fifth in class at Le Mans in 2018 alongside Pastor Maldonado and Nathanaël Berthon. Over the full superseason he took three podiums including a class win and pole, ending the season third in the LMP2 standings. He also raced in the 2019 IMSA SportsCar Championship, winning the 24 Hours of Daytona in LMP2.
The 2018–19 FIA WEC season also featured the 6 Hours of Spa-Francorchamps as a round; González took class victory there, adding a second significant 2019 win to his record. He returned to Le Mans in 2019 with DragonSpeed — this time alongside Maldonado and Anthony Davidson — but retired after 245 laps.
González joined Jota Sport for the 2019–20 WEC superseason alongside Félix da Costa and Davidson, and the trio became a stable combination. At the 2020 24 Hours of Le Mans the car finished sixth overall and second in LMP2 class. González ended the 2019–20 season third in the LMP2 standings with 152 points.
In the 2021 FIA WEC, still with Jota, González and Félix da Costa (paired variously with Davidson) recorded four podiums in six rounds, finishing third in the championship. At Le Mans 2021 the car finished eighth in LMP2 class.
The 2022 season brought the breakthrough. At the 90th 24 Hours of Le Mans — his sixth attempt at the race — González, da Costa, and Will Stevens finished first in LMP2 class and fifth overall. The three drivers then secured the 2022 FIA WEC LMP2 championship, González finishing first in the standings with 137 points from six rounds. His younger brother Ricardo had won the 81st edition of Le Mans in 2013 in LMP2, making the two brothers one of the few sibling pairings each to claim an LMP2 class win at the circuit.
Away from motorsport, González founded the Mexican investment management company Soliq and served as a board member of EPM, a cannabis-based pharmaceutical development company.