González was born in Havana, Cuba, on August 9, 1937. He received Bachelor of Arts and Bachelor of Science degrees from the Instituto de Marianao in 1954. Following three years of studies at the University of Havana, he attended the in Matanzas, Cuba, from which he received a Bachelor of Sacred Theology degree in 1957. He then studied at Yale University, receiving a Master of Sacred Theology degree in 1958, a Master of Arts degree in 1960, and a Doctor of Philosophy degree in 1961. He was the youngest person to be awarded the historical theology doctorate at Yale.
