A foreign national who is in Mexico as a Visitor can not register a vehicle in Mexico.

If the vehicle is in Mexico, and the owner has Temporary Residente or Permanent Residence status, the vehicle is deemed to be a "Chocolate vehicle". There is currently an amnesty to allow these vehicles to be legalized.

(A Temporary Residente or Permanente Residente may not bring a vehicle into Mexico using a Temporary Import Permit.)

https://mexicodailypost.com/2023/04/08/these-are-the-conditions-to-regularize-chocolate-cars-in-a-new-stage-that-begins-in-april-2023/

I received my Permanente Residente status earlier this year. Unfortunately, my vehicle was in Canada. I decided to import it (2007 Ford Ranger) into Mexico. It has been expensive and involved (approx $5,500 USD). I expect to complete the process, have the truck registered and licensed tomorrow. I will post a synopsis of the process in the next 10 days.