What's my next step?
There are different ways to skin a cat and they can all work to accomplish the same goal. If were doing this, this is the method that I would use.
Make sure that you have an Ethernet cable connected from an Ethernet port on the Google router to the WAN "O' Ethernet port on the Time Capsule. This connection must be maintained at all times.
Power up the Time Capsule and let it run for a minute or two
Hold in the reset button on the back of the Time Capsule for 7-8 seconds and release
Allow a full minute for the Time Capsule to restart to a slow, blinking amber light status
This action will reset the network settings on the Time Capsule so that it will pick up the new network settings that it needs from your new network. It will not affect any of the stored data on the Time Capsule hard drive.
Click on the WiFi menu at the top of your Mac's screen and look for a listing of New AirPort Base Station
Just below that listing, click directly on AirPort Time Capsule, or it may simply say Time Capsule

When you click on AirPort Time Capsule, that will automatically start up the Airport Utility setup 'wizard". The wizard will take a few seconds to analyze the network and then display a window that looks like the example below, except that you will see a Time Capsule pictured.

Network Name........Leave this setting alone for now. Later, we will turn off the WiFi on the Time Capsule so it will act only a backup hard drive
Base Station Name.....Type in a short name that you want to use for the Time Capsule
Password.....Type in a password that you want to use for the Time Capsule
Verify.....Type in the same password again to confirm
Click Next, and the setup wizard will configure the Time Capsule for you automatically. After a minute, you should see a message of Setup Complete and a green light will be displayed on the Time Capsule.
Click Done
Very important........Log back onto the Google WiFi network from your Mac
Click on the Time Machine "clock" icon at the top of the screen
Click on Back Up Now to start a backup
This may or may not work at this time
Post back on your results and we will know how to continue from this point