Your post is a bit confusing.
You don't need proof of purchase to unlock an Apple Account, as you don't buy Accounts.
Proof of purchase is only required if a device is Activation locked to an Apple ID who's password you don't remember. If your iPad is new, then this should not be the case, unless you logged in to your account on the iPad, and immediately forgot your email account, and then restored the iPad to Factory Settings using a computer.
Also, if you don't remember your email address, how do you know the account is locked? You only get the message the account is locked if you try to log in to the account, and for that you need to enter the email address so you must remember it.
The Apple Account being locked, has nothing to do with Activation lock of a device.
If you just need access to your Apple Account to set up the new iPad, then click here ➜ If your Apple Account is locked, not active, or disabled - Apple Support
If you don't remember its email, click here ➜ If you forgot your Apple Account primary email address or phone number - Apple Support
If the above is not helpful, then please clarify what is happening and what you are trying to do, and how the new iPad factors into this.