Forgot encrypted passcode for Apple ID after restore

Hello,

I have an iPod touch (5th generation) that I forgot the passcode to. I disabled it attempting to unlock it and restored it with recovery mode. I hoped that I would be able to load a previous back up and have my data back, but it seems that that only back up I created was made by the previous Apple ID used for the iPod.

Attempting to set up or otherwise connect the iPod to this Apple ID prompts to enter the original passcode, pre-restore. This is the only Apple device I own, so using the passcode from another device is out of the question.

Am I unable to log into this Apple ID on my iPod given that I don't remember this original passcode? Is it possible to load a back up onto my iPod using an Apple ID different than than the ID used to create the back up?

Thank you.