He served in the United States Army Air Forces from 1942 to 1945, after which he returned to his law practice in Brownsville, where he remained until 1961.
He served as Chief Judge from 1974 to 1979, when his service on the district court was terminated on August 1, 1979, due to elevation to the Fifth Circuit.
[1] Garza was nominated to the United States Court of Appeals for the Fifth Circuit by President Jimmy Carter on April 30, 1979, to a seat vacated by Judge Homer Thornberry.
President Jimmy Carter originally asked Garza to serve as the Attorney General of the United States, which he turned down.
Had he accepted and been confirmed by the Senate, Garza would have become the first Hispanic Attorney General of the United States.