You see, if you have shared resources (e.g., printers, network attached storage, etc...) on your network, you have to be on the same street (with different house numbers) in order to see and use network resources. If you have the same wireless network name (AKA 'SSID') and wireless password sprouting from both your gateway and Google WiFi, you probably won't have problems getting on the Internet, but you will likely have half your devices connecting to the gateway and half connecting to Google WiFi.
This is a problem because with home networking, you need to be on the same street to see each other on the network. Being on the same street on a network means that you have the same first three octets of your IP address the same. If you haven't changed or disabled the WiFi settings on your gateway before setting up Google Wifi, then half your devices may have an IP address that starts with 10 and half will have IP addresses that start with 192. If you have a wireless printer, it might end up with an IP address of 10.0.0.54 and if you're trying to print from a computer that has an IP address of 192.168.86.33, the computer will not 'see' the wireless printer, even though the wireless printer perceives itself to have a healthy connection to a network.
Possibly the most challenging part of this is locating your gateway's username and password combo. Don't forget to try the default of username: admin and password: password.