This link will take you to the various Mexican state offices that provide birth/death/marriage certificates. It is in Spanish but you can put it in google translate or another translator. You are looking to order a copy of the nacimiento (birth certificate). You do, of course, have to know the state of birth. As far as adoption is concerned and whether or not the original birth certificate is suppressed I really don't know for sure, but given that Mexico is lax on so many other things I would imagine they didn't go to the trouble to do this.

If there is a Mexican Consulate in your town I would also GO THERE and attempt to get the record. Many Mexican ex-pats get their birth certs from them for various reasons while living in the US. Mexican birth certs usually show at least 3 generations.

Also, if you want to wait or will manually browse the records yourself, familysearch.org has most civil records for Mexico births online starting in 1857, including birth certs. Some of them have already been indexed (by state) and others are awaiting indexing. https://familysearch.org/search/collection/list/?page=1&...