They process them through detention centers.

> I had to apply for a Green Card

Citizens of Mexico are not eligible for the green card lottery, so there is no way they can just "apply" for a green card. They would have to come on some kind of visa first.

> You can also apply for any work related visas that you qualify for

Most people do not qualify for any such visas. Mexicans can get NAFTA visas if they have the right kind of job offer (until Trump does away with NAFTA, of course), but those are nonimmigrant visas, and almost certain to be denied to people who have family in the US, since this would be taken as indication of immigrant intent.

>Or, you can marry a U.S. citizen

Difficult when you are living in Mexico.