Have you tried a FamilySearch center? (aka Mormon genealogy library.) They have thousands of locations around the world, so there is probably one near you.
If not, you can probably order microfilm from them directly. They have filmed millions of records in Mexico.
They also have many Mexico databases online, although most are not indexed and you have to browse them:https://www.familysearch.org/search/collection/list#page=1&a...
Hopefully, you can find his birth/baptismal record in these.