I'm familiar how ransomware works and how they encrypt the files.
If the encryption is done by a public key only (which the private is saved at the attacker's server), you cannot decrypt those files unless you receive the private key.
Which common bugs/backdoors the public decryptors found in the ransomware to be able to decrypt the files successfully? (https://www.nomoreransom.org/decryption-tools.html)
I can think about several - for example, if the encryption key is symmetric - one can try and catch it in ransomware's memory before it encrypts the file and use it to decrypt the rest afterward.