Marriage alone does not grant automatic legal status. The U.S. citizen spouse (21+) must file Form I-130 (Petition for Alien Relative). Processing times:
After I-130 approval, the beneficiary applies for an immigrant visa at the U.S. Embassy in Mexico City (medical exam, interview, background checks). This adds several months to years. Upon visa issuance, the immigrant enters the U.S. as a lawful permanent resident.
There is no shortcut solely through marriage while residing in Mexico; the standard consular process applies.