While there certainly are records of people in Mexico in the Spanish Archives, see the PARES website, such as the Pasajeros a Indias or the Casa de Contratación, sacramental records are kept at the local parishes, with some records, such as records of dispensations, kept at the dioceses in Mexico. It is possible that some of the older records have been transferred to the diocesan archives. There are also records of the Inquisition, I am not sure where these are held as I have never had occasion to use them.
Civil records of births, marriages, and deaths date from the late 1850s long after independence from Spain. These are all kept locally.