Secret... But generatable since 2009. [0] 2011 randomisation slightly reduced the risk, but not by much.
As many as 1 in 7 SSNs may have been accidentally used by more than one person. [1]
Unlike Australia's TFN or the UK's VAT, SSN has no self-check, making it rather easy to just... Generate one that works.
And all an API check of the number will tell you, is what an attacker would already have: DOB and Place of Birth.
[0] https://pnas.org/doi/full/10.1073/pnas.0904891106
[1] https://www.nbcnews.com/technolog/odds-someone-else-has-your...