US immigration, I-130, I-485, how long social security process

You AND your fiance need to speak with an immigration lawyer - filing based on marriage to a permanent resident is very different than filing based on marriage to a citizen, and has practical implications that may make it unrealistic for someone in your situation.

Unlike a filing based on marriage to a citizen, where you can file both forms together and you need only have entered the country legally even if you are without currently valid status, in a filing based on marriage to a permanent resident you need to file the I-130, get an approval, and then wait until the priority date is current before you could process the final stage. Right now, this wait is almost five years for most people - probably longer if you were born in Mexico.

Generally, there are two ways to process the final stage of a permanent residence case: an I-485 Adjustment of Status application here in the U.S., or processing through the U.S. consulate in your home country or country of last residence abroad.

Here's where the big problem comes: you can't file the I-485 to Adjust Status in the U.S. since you have been out of status - this is forgiven for spouses of U.S. citizens (if they at least entered legally) but not spouses of permanent residents. This leaves processing through a consulate abroad - but if you have been here more than one year since the expiration of the H-4 as you say, the act of leaving subjects you to a TEN YEAR BAR to coming back into the U.S. - so you can't really do this either in most cases. Sort of a no-win situation.

Some people might have ways around these problems - if a green card case was filed for you before April 30 2001, you may be eligible for a provision that lets you just pay a penalty and adjust here if that earlier case was approvable at the time it was filed. And in some circumstances there may be a way to get a waiver for the ten-year bar (though even where a viable situation exists, it is difficult and risky).

A better option might be to see whether your fiance is eligible for citizenship, and if so perhaps have her apply and then process you as the spouse of a citizen rather than a spouse fo a permanent resident.

Until the best method of actually getting you to a place where your status is protected in the U.S. is determined - either by processing outside through a consulate as a spouse-of-permanent-resident with a waiver of the ten-year bar, processing here through an I-485 as a spouse-of-permanent-resident with eligibility for the penalty provision based on a pre-April 30, 2001 case, or processing here through I-485 as a spouse-of-[eventual]-citizen - I can't really answer your question on when you would be eligible for a social security card.

If you process abroad, it probably wouldn't be until reentry on the green card; if you process here, it would be about three months after the I-485 filing when you got an employment authorization card - but no telling how long any of these things would take without evaluating your case.

Again, I strongly suggest that you and your fiance speak with an immigration lawyer to sort out the possibilities.

Good luck!