Your iPhone could not be activated because the activation server cannot be reached

Solution 1:

Since you have an iPhone 7/Plus i immidiately suspect one of the many chip problems plauging those two models (actually the problem is with the motherboard substrate itself, I think).

If it is this one problem, you can find out by jumping to the initial "Hello" screen after the update, if you have that, and selecting the info i in a small circle in the bottom right corner. It will show you various hardware parameters of your phone, such as the serial number. It should also show the IMEI and a few others it gets from the mobile network chip (as far as I understand).

If it is unable to retrieve one or more of these parameters from the hardware, which is a common affliction of the iPhone 7 series, you will not see them in that info screen and it will not be able to activate, and you might get the error you are reporting, despite it managing to reach the activation server. The problem is rather that it doesn't manage to give the activation server the info it is requesting.

If you find that this is indeed the case, nobody is able to fix your phone but Apple, but you might be able to get a free service if you can convince them that it is the same problem essentially (which it is), as the one they have a free program for: https://support.apple.com/iphone-7-no-service