My wife and I are preparing to the last stage of obtaining Green Cards (filing the adjustment of status).
How long would my wife wait to get her SSN? (I have mine already.)
Based on the information in the Application for Social Security you should be able to receive one 7-14 days from the moment the application is filed.
16 Show an address where you can receive your card 7 to 14 days from now.
When filing Adjustment of Status, you should also at the same time file for EAD (for work) with form I-765 and Advance Parole (to allow you to leave the U.S.) with form I-131. These are free to file for as an Adjustment of Status applicant. The EAD and AP will usually be received within 3 months.
When you have the EAD or green card, you can apply for a Social Security Number. And it takes 3 months at most that you would get one of these.
It is not quite clear to me which adjustment of status you are talking about. Is this from fiancee visa to provisional resident? Or from provisional resident to permanent resident?
When we moved to the US (before moving to Indonesia), we applied even before she got her green card. Basically as soon as you have the work permitted stamp in her passport, the application can begin. This will usually be before you get the actual green card. Of course my wife came in on a spouse visa, so it might be different with a fiancee visa, but the general approach should be the same. Once you have something which says that processing for the green card has begun, and that work is permitted, go for it.