Procedure of getting married and getting a green card.

But I know a couple that made it that way, the thing was that he never had a visa, so she hired a judge to go to the bridge and marry them, then (I don't know how) she got him a green card.
The difference here is that I do have a visa but I wouldn't cross to avoid lying on my intentions.

I don't know. If you don't enter the US then I would assume an American marriage license is invalid.
 
If you really care about marrying in the US vs Mexico, then you can try to go to the US with the visitor visa, marry, and shortly afterwards go back to Mexico to do Consular Processing. You'll be perfectly honest with your intentions, and if they believe you, they will let you in. (Of course they might not believe you and not let you in.)

I guess if you've crossed the middle of the bridge but haven't gone through immigration yet, you're in US territory so technically you should probably be able to use a US marriage license, but that seems like a ridiculous plan.
 
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