Blanco was born in Mexico City, in the district of Tlatilco, but grew up in Tepito. Born to Faustino Blanco and Hortensia Bravo, he was named after the last Aztec emperor Cuauhtémoc, in which the name means “one who has descended like an eagle”. Ángel González, a scout for América, discovered him as he won the Torneo Benito Juárez as a part of the Distrito Federal selection team, and brought him to Club América’s development program. Having played most of his career in América, with 333 appearances and 135 goals, Blanco has become an idol to the club’s supporters and an important figure in the history of the team. Blanco made his debut in the Mexican Primera División in 1992 at the age of 19 with América. He won his first Golden Boot with 16 goals in the Winter 1998 season for Las Aguilas. He was loaned for Winter 1997 and Summer 1998 at Necaxa, in which he scored 13 goals in 28 appearances. Blanco was later loaned to Real Valladolid of La Liga for the 2000–01 season. However, he suffered a broken leg while on international duty which kept out of the side for six months. Blanco returned to Valladolid for another loan spell the following season, but he struggled with homesickness and regaining his form. He had a knack for scoring great goals in La Liga, with most notable, a free-kick against Real Madrid at the Santiago Bernabéu Stadium, he returned to Mexico. Blanco spent the 2004 Apertura season with Veracruz, where they ended up winning their group, but were defeated in the playoffs by UNAM. Blanco was a popular player during his time there. In May 2005, Blanco won his first club championship as a player, leading Club América to its tenth league title, when Club América defeated U.A.G. by an aggregate score of 7–4 (1–1, 6–3). In the next three consecutive years between 2005 and 2007, he was awarded the MVP. He scored his final goal during the championship final against Pachuca in 2007.