If the Netgear is truly only a modem, then OP needs the Google router. The modem doesn’t create a network; it’s just the gateway to OP’s ISP. Therefore, the only device that should be plugged into the modem is a router.
For example, my setup for Xfinity is an Arris Surfboard modem to an EdgetouterX router to a Unifi 16 port switch then to all of my devices including 2 Unifi APs. I can’t connect a laptop or anything else into the 2nd port of the Surfboard modem.
My response was the solution. You cannot connect directly to a modem and get internet access or create a network. You must have the router also. For many ISPs, they say they provide the modem but it’s actually a modem and router. In your case, your Netgear is only a modem so you have to have the Google router in order to have access to the internet or create a network.