Airport Time Capsule Third Generation Roaming connection with a Google wifi router
Roaming doesn't work perfectly between multiple brands of products, and wireless roaming (which you may have been reading about) definitely doesn't work between the Apple Airport units (Time Capsule included) and any other non-Apple products.

However here is what you would want to do in your situation to make things a little easier.

1) Make sure the ethernet cable comes from your Google WiFi Router and plugs into the WAN plug of the Time Capsule (that's the one at the very bottom, or on the one side with the little circular icons above the port.

2) Go into the Airport Utility and configure your Time Capsule settings as such:


Wireless tab -- Network Mode: Create a wireless network
Use the same exact Wireless Network Name as your Google WiFi
Use the same exact Wireless security settings as your Google WiFi -- typically WPA2 Personal and the exact wifi password.
Network tab -- Router Mode: Off (Bridge Mode)


Note: You may need to occasionally turn off and on your WiFi on your device to get it to join the closest wifi connection. As long as your WiFi settings are the same you should not need to re-enter any name or password info when the device tries to reconnect. The only way around this issue is to get another Google WiFi product to extend your network. Mixing brands tends to give finicky behavior for things like roaming between WiFi access points.