How to unlink Apple ID from a MacBook Air?

You must contact the generous giver or the previous owner.

Each Apple device is linked/associated with an Apple ID of the person who did the setup.

Activation Lock prevents anyone who is not the owner from using this Mac.

To unlock the Mac, you need the Apple ID and password of the previous owner, that were used during set up.

So have to contact the previous owner.

The previous owner has to read -> What to do before you sell, give away, or trade in your Mac

What to do before you sell, give away, or trade in your Mac - Apple Support

Then the previous owner has to remove the Mac mini from his account, see this Apple article:

Check your Apple ID device list to see where you're signed in

Check your Apple ID device list to find where you're signed in - Apple Support

Then you can sign in with your Apple ID.

See also -> Activation Lock for Mac -> Activation Lock for Mac - Apple Support

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Other ways to disable Activation Lock

• If you don't have access to your Mac or the settings above, use a web browser on another device to remove Activation Lock on the web.
• Activation Lock is disabled when you use the Erase All Content and Settings feature.

If your previously owned Mac shows an Activation Lock window that asks for someone else's Apple ID, the previous owner may need to remove Activation Lock for you.

You can also contact Apple support for help, -> Get Support (apple.com)

You have to show proof of ownership of your product, provide all documentation showing your purchase of the device.

If you do not have additional proof of ownership, contact the reseller. They may be able to provide the original purchase document.

Once Apple receive your proof of ownership, Apple will further review your request and provide an update.

See also -> Keep your receipt after you buy an Apple device

Keep your receipt after you buy an Apple device – Apple Support (UK)

If you can't get in touch with the generous giver or the previous owner, you can't use the Mac.