From 1975 to 1977, he completed a postgraduate degree in Moral Theology at the Academia Alfonsiana in Rome, belonging to the Pontifical Lateran University.
The Archbishop of Asunción, Ismael Rolón Silvero gave him his holy orders in the Metropolitan Cathedral on 15 August 1982; co-consecrators were the then Auxiliary Bishop of Asunción Jorge Adolfo, Carlos Livieres Banks, and Aloísio Ariovaldo (Tarcísio) Amaral, then Bishop of Limeira, São Paulo.
In 1989, he was elected administrator of the Archbishopric of Asunción "ad interim", shortly thereafter in 1990 to prelate the Roman Catholic Diocese of Ciudad del Este.
In November of that same year, Pope John Paul II appointed him Apostolic Administrator of Caacupé.
[1] His suffragan bishop, Rogelio Livieres Plano publicly claimed in 2014 that Cuquejo was homosexual, which caused a scandal in Paraguay.