Sorry, but this seems to be the only way.
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Turn off Activation Lock before you send your Mac in for service, sell it, or give it away
Before you send your Mac in for service, sell it, or give it away, you should turn off Activation Lock. If you have access to the device, turn off Find My Mac to disable Activation Lock, and then sign out of iCloud.
- Choose Apple menu > System Preferences.
- Click Apple ID, then click iCloud.
- Turn off Find My Mac.
- Click the Sign Out button.
If you can't access your Mac and you need to turn off Activation Lock, follow these steps.
- Go to iCloud.com and sign in with your Apple ID.
- Click Find iPhone.
- Select All Devices, then click your Mac.
- Click Erase Mac. Select Next until the device is erased.
- Click
next to your Mac.
What to do if your Mac starts up to an Activate Mac window
If you've purchased a Mac from someone other than Apple or an authorized Apple reseller and the device starts up to an Activate Mac window, the device is still linked to the previous owner's account. You'll need to ask them to remove the device from their account.
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copied from: About Activation Lock on your Mac - Apple Support
However, you might try to call Apple Support about that. Since they are able to help you to disable the Activation Lock on your iOS device, if you show them the original purchase receipt, maybe there is a similar way for the Mac.
Get Apple Support
Contact Apple for support and service - Apple Support