I'm looking for some clarification on whether or not I'm correct in how I'm thinking about this.
From my understanding of RSA, the public key gives you the value $n$ (large prime $p$ times large prime $q$) and the value $e$ (a value less than $n$ which is not a factor of $(p-1)(q-1)$).
The way to try to crack a ciphertext according to the RSA problem is by using the values given to you in the public key (demonstrated in this answer). However, if an attacker only has an encrypted message without the private key (an example would be getting into a system and obtaining an encrypted file but the keys were in "Cold Storage"), he/she wouldn't be able to perform this attack.
While it's possible to recover the public key if you know the ciphertext and the plaintext, given only the ciphertext, it is likely much more difficult (if not almost impossible) to find the correct prime numbers, the value $e$, and the value $d$.
Am I correct in this assumption?
Side note: I know that the public key is named "public" for a reason, but for the sake of this scenario, just assume some situation like the one presented above.