I am very puzzled. I tried to replicate your issue (no response to REGISTER from Asterisk but ok from PhonerLite). I don’t have a Telmex account, so just tried +525522223333 and a dummy password.
Indeed, there was no response on my test system in Google Cloud. But unfortunately, there was also no response in PhonerLite. Possibly, requests with an invalid username are simply discarded.
It seems that you are not alone; see https://asteriskmx.org/foros/forum/asterisk/instalación-y-primeros-pasos/38921-configuracion-de-troncal-freepbx-telmex . Using that proxy, I did get a 403 with a Warning header showing “invalid user”, but don’t know whether that proxy would be valid for your account.
You posted in an old thread about a specific Italian provider. Try starting a new thread with Telmex in the title – with luck a Telmex user who has solved this will respond.
If not, one approach would be to copy a successful initial register to a file and send it with sipsak. Assuming that you get a response, gradually change it to what Asterisk was sending, one header at a time, testing after each change. Once you learn which header is the culprit, you should be able to change the Asterisk config to fix the problem.