It is logistically impossible for an entire country of 300 million to do that in any reasonable timeframe.
The only two options going forward are: (1) abandon SSNs as a method of identity verification and switch to something better, (2) drown in continuous scams and identity theft forever.
Since the former requires a government that is competent at governance and a population that can adapt to basic administrative changes, the US is now stuck with the latter for the foreseeable.