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No, You have to begin in the country of your origin. 
You can come in on a six month VISA leave for a day and return again for six months.  Very easy.

Welcome to expat Mexico Paul 123
Thats a very interesting question. Given that there is a Mexican consulate I would start by posing that question to them.

Things have changed everywhere. Yes you need to start in the U.S. if you want to apply for any type of residency, but you can visit Mexico, which given the status in the U.S I would do if I were you.They will look at the time you spent visiting Mexico when they consider your application.

The visitor visa can be for up to six months before you have to exit to renew. I say up to 6 months because how long is entirely up to the border agent. When you need to renew I would not just try to exit and come back the next day. They don't like that. If you are entering and leaving via T.J. You could just go back and forth. Because there are still a lot of people in T.J. who work in the U.S. so far.
Things have changed from month to month.

Currently they are talking about having phone service providers demand a facial recognition and iris scan to get a new account. Thats not going over too well with the providers or their clients so I don't know if it will happen before you visit.

Good luck

Mexican Embassy not a Mx. Consulate.

jp91460 wrote:

No, You have to begin in the country of your origin. 
You can come in on a six month VISA leave for a day and return again for six months.  Very easy.

I did researched and this is not the case. Can apply at any consulate in any country not only your country of citizenship.

The dilemma is the country you reside in doesn’t have a consulate and all borders are closed or require quarantine.

Paul123 I am currrently living in Huatulco Oaxaca. I came here from Canada.  I am in conversation with an immigration counselor and will apply for residency june 1. i will know more after that. In the past one has always needed to apply from outside Mexico. i however recently spoke with a couple that were able to apply and recieve 4 year temporary residency from within Oaxaca. Theirs may be a special case as perhaps extenuating reasons why not able to return to home country. After conversation with them seemed like worth a try for me. But indeed this is not the norm and if you can, go to whatever mexican embassary is near you. Other option is come to Mexico and than apply in neighboring country like Belize, USA, I would recommend somewhere in Texas, or Guatemala.  Best of luck,  Buena Suerte