Trying to turn off Activation Lock but only remember the month and year it was bought.

You may already be aware of some of the following - but for completeness...

Here are the Apple support pages that outline the Activation Lock - and the only mechanisms by which it can be satisfied:

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Turn off Activation Lock – Apple Support

As you will discover, unless you are the owner of the AppleID that was last used to activate the device, you’ll not be able to defeat or bypass the Activation Lock. With documentary evidence that you are the original owner (such as sales receipt showing the serial number), Apple may be prepared to assist - otherwise they and nobody here will be able to help you.

If you have the necessary documentation, Apple have introduced a portal though which you may be able to request release of an Activation Lock:

How to remove Activation Lock - Apple Support & start an Activation Lock support request.

AppleID

You may also need your AppleID and associated password. If these have also been forgotten, they can be recovered here:

https://iforgot.apple.com

To recover your credentials, you’ll need access to one of the following:

• Your primary email address mailbox that corresponds with your AppleID
• Any of the secondary/recovery email addresses that should be configured for your AppleID account
• Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID

More information about recovery of your AppleID and associated Password:

If you forgot your Apple ID - Apple Support

If you forgot your Apple ID password - Apple Support