Both his father and grandfather arrived in South America in the fleet led by Pedro de Mendoza.

In 1598, at the age of 23, González was ordained a priest by Bishop Fernando Trexo y Senabria of Córdoba, to serve that diocese.

[2] In the region of Iyuí, he had difficulties with the local chieftain and sorcerer (cacique) Nheçu (written Ñezú in Spanish), who opposed the missions.

On 15 November 1628, while preparing to oversee the installation of a new bell for the church at the Mission of Todos los Santos de Caaró, González was struck down and killed with a tomahawk, along with his fellow Jesuit, Juan del Castillo, upon the orders of Nheçu.

He and his companions were later canonized by Pope John Paul II in Asunción, thus becoming the first native of Paraguay to be declared a saint by the Catholic Church.