Device Not Eligible for AppleCare message why?

Bought from where exactly?

When buying directly from Apple you have 60 days from the date of purchase to buy Apple Care+.

When buying from a 3rd party, that is not an authorized Apple reseller, the time starts when they get it from Apple, not when you get it from them.

Why did it take you a month to set it up?

AppleCare+ coverage is available to buy when you purchase your device, or for a limited amount of time after.

If you can’t see AppleCare+ coverage available, check that your device is eligible.