The SSN itself is limited to under 1 billion possible permutations anyway because the format is 9 total digits. (3 digits hyphen 2 digits hyphen 4 digits.)
And if I recall they also have something weird with the state you were born roughly corresponding to which 3 digit prefix you’re issued. Obviously that isn’t purely true either because that would only give you about 1 million unique numbers per prefix.
Either way they’ve gotta be close to the theoretical maximum of the format without recycling numbers.