Born in Mexico City, Mexico, on September 16, 1969 to Rafael and María Guadalupe Avilés, he joined the Congregation of the Oratory of St. Philip Neri in 1986. 

His studies for the priesthood began in Mexico City and continued in Rome, where he earned bachelor’s degrees in philosophy and sacred theology from the Pontifical Athenaeum Regina Apostolorum. He also holds a master’s degree in education administration and supervision and is a certified teacher in the State of Texas. 

Bishop Avilés was ordained to the priesthood on July 21, 1998, at the Basilica of Our Lady of San Juan del Valle – National Shrine in San Juan, Texas. Following ordination, he was appointed parochial vicar at St. Jude Thaddeus Church in Pharr, Texas. He also served as a teacher and principal at his Congregation's school. 

In 2002, he was appointed pastor of Sacred Heart Church in Hidalgo, Texas. From 2000 to 2012, he served as a member of the Permanent Deputation of the Confederation of the Oratory of St. Philip Neri, and in 2012, he was elected Procurator General. 

On December 4, 2017, Pope Francis appointed him Auxiliary Bishop for the Diocese of Brownsville, Texas. He was consecrated on February 22, 2018, at the Basilica of Our Lady of San Juan del Valle – National Shrine in San Juan, Texas. 

On December 1, 2025, Pope Leo XIV appointed him as the 9th Bishop of the Diocese of Corpus Christi.