Both Atlético Madrid and Cádiz CF became interested in acquiring González in 1982 – despite the "Colchoneros"' higher profile, he signed with the Andalusians. His first game in Spain came in a friendly against "La Barca de la Florida", while his Segunda División debut was on 5 September 1982 in a 1–1 home draw against Real Murcia, scoring in the process. He became a fan-favorite thanks to his dazzling moves and goals, but was also notorious for his love of the nightlife and his sleeping habits were also brought into question, whilst his on-field abilities endeared him to the Cádiz fans enough that they overlooked his minor indiscretions; he finished his first season with 33 games and 14 goals as the team promoted to La Liga.