Solá became the manager of Puebla in 2006, but was sacked twice during his tenure, only to be brought back after the players requested he be reinstated. During his time at Puebla, Solá gained tremendous popularity in Mexican football, having saved the team from being relegated to the Primera A and being successful with a "small club".
"Chelís" was publicly supported by the players, front office, and the government of the state led by Mario Marín, since they believed he was the main reason why Puebla, after over 15 years, had a competitive team again. Sánchez Solá led Puebla during their highly-successful Clausura 2009 campaign rub. After finishing fifth in the general table, the team eliminated Monterrey in the quarter-finals, but was eliminated in the semi-finals by Universidad Nacional Autónoma de México UNAM.
A few days after the playoff match against Club Universidad in 2009, Sóla appeared in a political ad by the Partido Revolucionario Institucional (P.R.I.), the political party of Puebla's governor at the time Mario Marín. This resulted in criticism from some Mexican sports commentators and others who disagreed with sports figures getting involved in political campaigns.