When you say that you forgot your recovery key, are you telling us that you turned on FileVault?
If so, there is no way to unlock the FileVault-encrypted disk for which you have forgotten the user name, password, and recovery key, to retrieve your data. When you enabled FileVault, you had a choice of recovery methods: one of them being to allow recovery using your iCloud (Apple) account; the other being to use a recovery key.
Turning on FileVault means that you can't simply boot up into single-user mode to get access to the drive, and the choice you made to use a recovery key means that even Apple cannot help you now that you have forgotten it.
Mac Help – Encrypt your Mac data with FileVault [High Sierra] – Apple Support
"WARNING: Don’t forget your recovery key. If you turn on FileVault and then forget your login password and can’t reset it, and you also forget your recovery key, you won’t be able to log in and your files and settings will be lost forever."
You may be able to reset and wipe the Mac, but the FileVault-protected data is gone. Hopefully you kept backups.