I'm assuming that her father satisfied the transmission requirements (over 5 years of physical presence [not just residence] in the US before her birth, and at least 3 of those years after the age of 14)? If so, she can try applying directly for a US passport (with or without the certificate of citizenship).
Because her birth was never registered, USCIS has no record of her being a citizen, hence her LPR status (I've heard stories where citizens born abroad were even issued non immigrant visas and be in that status for years, or even deported before they made the claim to citizenship), but it doesn't change the fact that she was a citizen from birth, simply that she would have to make that claim (through US passport or filing the N-600).
il.usembassy.gov/u-s-citizen-services/passport-services/first-time-passport-adult-not-yet-documented-u-s-citizen/