There is nothing you can do.
If you don't have your recovery key (you had to generate it yourself as its not automatically generated, and were told to write it down and keep it safe when you did so) and you don't have another device already signed in to your Apple ID from which you can generate a new one, then you are now permanently locked out of your Apple ID. Apple cannot help you at this point.
click here ➜ Set up a recovery key for your Apple ID - Apple Support
When you generate a recovery key, print a copy or write it down. Keep it
in a safe place, so that you always have access to your Apple ID. You
can give a copy of your recovery key to a family member, or keep copies
in more than one place....
...However, if you lose your recovery key and can’t access one of your
trusted devices, you'll be locked out of your account permanently.
Your only real option is to just create a new Apple ID to use with your iPod.