How soon can a foreigner begin working if they entered the United States with a valid travel visa then married a United States citizen and filed for adjustment of status immediately?

As soon as they get a residents Social Security number. Here's a little more detailed answer than the above statement for you: The alien has to file a petition for an EAD or Employment Authorization Document by using USCIS form I-765. Once this document is approved you will get a mailed copy to you and you can take that and work. I believe once you get your green card at that point you can apply for an SS#. If you married a US citizen while here on a B-2 (visitor) visa then this process takes anywhere from three months to nine months. But of course, the US govt has been known to lag and maybe can take up to a year I've heard.