Activation server is temporarily unavailable

Apple sent me an article trying to help me fix my phone: If you see No Service or Searching on your iPhone or iPad - Apple Support

I did everything in the article that was sent to me and nothing worked. So I did the last option, I tried to restore my device. But it won’t let me back in. It just says “it may take a few minutes to activate your iPhone.” then says “Your iPhone could not be activated because the activation server is temporarily unavailable. Try connecting your iPhone to iTunes to activate it, or try again in a couple of minutes. If this problem persists, contact Apple Support at apple.com/support." When I try connecting through iTunes it says “The iPhone could not be activated because the activation information could not be obtained from the device. Disconnect your iPhone, make sure the SIM card is inserted correctly and, if you use a SIM PIN, tap Unlock to enter it, and then reconnect your iPhone.” I spent an hour at Verizon today where we installed a new SIM card, it is definitely not the problem. Now I am completely without a phone. Stuck on the activation page that says “Hello"

How can I restore my phone from the backup if I have no service?