The Norton core is just a WIFI router. It will work because you'll still have the cable modem (SBG6900-AC) cable modem to terminate the connection from Cox.
As for bridge mode on Arris it's a pain sometimes. Sometimes works and sometimes it doesn't. You may be better off just having the SBG6900-AC as a router using IP 192.168.0.1 and set the Norton core as 192.168.1.1 and turn off the wifi connection on the SBG6900-AC. Everything inside your wifi and wired network after the core will be 192.168.1.1 so make sure you update any printers or any other devices that have a static IP.
It will be setup this way. Cox cable wire goes into the SBG6900-AC then you plug a cat5e (cat6) cable from the SBG6900-AC to the Norton Core. Set the Norton Core default IP to 192.168.1.1. The SBG6900-AC default IP is 192.168.0.1 unless you changed it.
Cable wire ------SBG6900-AC (Disabled Wifi)---------Norton Core
Make sure the DHCP on the SBG6900-AC is set to the 192.168.0.100 and up range or just turn it off all together. However, it's good to keep it enabled while you're setting it up so it will pull from the SBG6900-AC while you're setting it up.
Then set the static IP on the Norton Core as 192.168.0.2.
Once you have the static IP on the Norton Core from the SBG6900-AC you can disable DHCP.
If you need to do any port forwarding you want to port forward on the SBG6900-AC to the 192.168.0.2 IP and then inside the Norton Core you port forward as normal.
You could also just put the Core in the DMZ on the SBG6900-AC but I personally feel it's better security to have nothing in DMZ.
Side note, I don't work for Cox just do networking for a living.