General Discussion

Been in IT for 31 years. My assumption is they would write it in a newer code on a unix or system with all new hardware.
The existing system is in COBOL on a mainframe system.
I'm dramatically oversimplifying it. You could literally write a PhD thesis paper in Computer Science on the Social Security system and I'm sure people have in the past. I cannot express enough how complicated a system it is and how complicated it would be to stand up a new system with fresh code and hardware. I am honestly am not even sure it's possible. A project like that would be legendary. It would take an army of programmers and project managers and a host of other people years to do it and it still likely would not work.
The existing system has been built up and tweaked and updated and curated for decades.

No sane person, who had any idea what they are talking about, would ever imply they could do it in a month.