He was appointed governor of Spain's New Mexico colony and installed in that office in late November 1634, succeeding Francisco de la Mora y Ceballos.
Once in power, he organized a series of commercial companies, paying little attention to his duties as governor in the province, such as that of maintaining peace between settlers and Native Americans.
[2][3] Martínez de Baeza took little interest in the Franciscan missions, making it difficult for them to convert indigenous people to Christianity.
However, Baeza asked Quirós to show him some evidence so he would know what he was saying was true, because he knew that the Franciscans had decided that conversion to Christianity should to be done in the apostolic way, by persuasion, and never using military force.
Meanwhile, Martínez de Baeza wrote a series of reports containing false information about certain individuals of the clergy in order to discredit them in the eyes of the viceroy.