No it's not normal unless you live in an area that usually has connectionn Issues. If you are within the 14 day exchange period have them exchange it for a new device. You can also contact (or visit) Apple to see if it needs to be replaced under warrant.
The iphone 7 has had many issues with the Verizon network. It will not work with the network.
I was able to get customer service to allow me to return the phone out of the return period.
The phone flat out is not compatible with the network.
Not exactly true. I have 4 iPhone 7's that work perfectly fine on the Verizon network. I know many other people with 7's on the Verizon network and they have no troubles either. So telling people that it will not work on the network is a false generalization. It didn't work for you and it's not working for some but it is not something that absolutely won't work on the network which makes me think there is something other than a network issues. The people I know in my area with their iPhone 7s are all on AT&T so it's clearly not a Verizon only issue.