You can't easily do that without experiencing something called double NAT. The recommended thing to do is remove your other router and just use Google Wifi as your router, letting it handle DHCP and all other services, but it sounds like you don't want to do that? If that's the case, are you able to put your other router into bridge mode?
Bridge mode - Google Nest Help
If you can put your other router in bridge mode, the routing part (NAT) gets turned off. Your primary Google Wifi point will then handle the routing (NAT and DHCP etc) for your network. It's also recommended that you would then turn off the Wifi on your other router, and just connect all your devices to Google Wifi. Your devices would all be in the same subnet and be able to connect to each other. Your other router just becomes a bridge/gateway to your ISP.
You can put your primary Google Wifi point in bridge mode, but that only works if you're only using 1 Wifi point. If you're creating a mesh network, you can't put Google Wifi into bridge mode.
Strictly speaking, you can set a custom LAN subnet in the Google Home app settings. You could configure Google Wifi to hand out addresses in the same subnet range as your other router, but it's not recommended. This would only really work if you're using static IP addresses with all, or the majority of, your devices. The reason it's not recommended is because the two routers don't have a way to share with each other what IP addresses they've issued to devices, so you are highly likely to end up with IP address conflicts. You'd also need to setup the pool of addresses Google Wifi issues such that it excludes the IP addresses issued to your Wifi points themselves. Similarly again on your other router, you'd need to exclude the IP addresses assigned to your Google Wifi points.
Set a custom LAN IP - Google Nest Help
Of course, if you're not connecting any devices to your other router (other than Google Wifi), then this might not be such a problem for you. Sometimes double NAT doesn't cause you any issues, it depends how you're using your Wifi network.
Fix Double NAT when two routers run at the same time - Google Nest Help
