Activation Issue

Did you try activating your phone via iTunes, as mentioned in the article?

If you still can't activate, here's how to activate your iPhone through iTunes instead:

1. Make sure that you have the latest version of iTunes.
2. Check that your computer has an Internet connection.
3. Open iTunes on your computer. With the cable that came with your iPhone, connect your iPhone to your computer.
4. Wait while iTunes detects and activates your iPhone: 

• • If iTunes shows, "Set up as New" or "Restore from Backup," it means that iTunes activated your iPhone. 
  • If an error in iTunes says that the SIM card isn't compatible, contact your carrier.

Start here: If you can't activate your iPhone - Apple Support

Did you try restarting your phone, as mentioned in the previous article and the one below?

iPhone not activating; “we’re sorry, we are unable to continue with your activation at this time.” error fix - AppleToolBox

So you aren't seeing this "an alert says the activation server is unavailable" that is in the first sentence of that article?

It states right at the top of the article, "If your iPhone can't be activated or an alert says the activation server is unavailable or the SIM card is unsupported, learn what to do".

That is a different matter. Has this iPhone ever been jailbroken or has your computer ever been used with a jailbroken iPhone?

Give AppleCare a call and see if they can spot the issue on their end.

You didn't waste my time at all, sorry we weren't able to resolve your issue.