No, it is not legally possible to marry in Mexico at the age of 16. Mexican federal law establishes the minimum legal age for marriage at 18 years old for both men and women. This law applies nationwide, without exception for parental consent or judicial approval at that age.
Prior to a 2019 federal reform, some state codes allowed marriage at younger ages with parental consent, but the current general law sets a firm floor of 18. Anyone considering marriage in Mexico should verify the most current requirements with the local Civil Registry Office (Registro Civil) in the specific municipality where the ceremony would take place.