The iPhone 7 Plus has two model versions.
The A1661 is the GSM+CDMA model and works on pretty much any carrier, including Verizon and Sprint. The A1784 is the GSM-only version, sold as the carrier model for AT&T and T-Mobile, and won’t work fully with CDMA networks.
I suspect that your model is the A1784 that is designed to be ONLY on a GSM network such as AT&T and therefore will not work on a CDMA network that Verizon uses.
You can check the model number that you have by going to Setting-->General-->About and look under Model Number. If you see a model number starting with a M then just tap on that number and it will display the model number beginning with an A.
Axel F.