On January 1, 1964, shortly before turning 14, he entered the Seminary of Morelia where he studied humanities, philosophy, and theology.
González made specialized studies at the Escuela para Formadores in Toluca, an extension of the faculty of psychology of the Pontifical Gregorian University of Rome.
On March 18, 1999, Pope John Paul II appointed him titular bishop of Voncaria and auxiliary of Morelia.
As Auxiliary Bishop he was in charge of the permanent formation of the Morelia clergy and member of the Episcopal Commission of Indigenous Pastoral for the triennium 2004-2006.
On June 9, 2006, Benedict XVI appointed him as Bishop of Tapachula, which he held until 2017, when Pope Francis named him Archbishop of Acapulco.