González made his Formula One debut at the 1950 Monaco Grand Prix, driving for Scuderia Achille Varzi. A close friend of Juan Manuel Fangio and fellow Argentine competitor Roberto Mieres, he competed in 26 World Championship Formula One rounds between 1950 and 1960, with gaps during which he raced primarily in endurance and non-championship events. His final Grand Prix was the 1960 Argentine Grand Prix.
Across his 26 championship starts, González scored two victories, seven second-place finishes, six third-place finishes, three pole positions, and six fastest laps, accumulating 72 and one-seventh points under the scoring system of the era.
The defining moment of González's career came at the 1951 British Grand Prix at Silverstone, where he drove for Ferrari and won the race — scoring the first Formula One World Championship victory in the constructor's history. The result established Ferrari as a genuine challenger to the dominant Alfa Romeos of Fangio and Farina, and announced González as a driver capable of beating the best in the world.
The 1954 season was González's most successful in Formula One. He finished runner-up in the World Drivers' Championship with Ferrari, behind champion Fangio, recording his second Grand Prix win at the British Grand Prix at Silverstone — making him a two-time winner at the same circuit. He also won the Portuguese Grand Prix for Ferrari that year.
Beyond Formula One, 1954 brought González a landmark endurance victory: he won the 24 Hours of Le Mans with co-driver Maurice Trintignant in a Ferrari, cementing his reputation as a versatile competitor across different racing disciplines.
González won the 1951 Coppa Acerbo, a prestigious pre-war Italian road race that survived into the early championship era. He also won a number of non-championship events including the Grand Prix of Buenos Aires in 1951, the Rio de Janeiro Grand Prix in 1952, and the Glover Trophy in 1952. In endurance racing, he placed in the 1000 Miles of Buenos Aires in both 1956 and 1960, and won the 500 Miles of Rafaela in both 1958 and 1959.
On 10 July 2011, during the British Grand Prix weekend, González was honoured by Ferrari and the FIA on the 60th anniversary of Ferrari's first Formula One World Championship victory. As part of the celebration, Ferrari driver Fernando Alonso drove González's original Ferrari 375 F1 for four laps around Silverstone. Later that day, Alonso won the British Grand Prix in his contemporary Ferrari, a coincidence that gave the occasion additional symmetry.
González died in Buenos Aires on 15 June 2013, aged 90, following respiratory failure after a period of declining health that had begun with a heart attack earlier that year.