You need to create a GKE cluster in an existing VPC that is accessible from...

Creating GKE private clusters with network proxies for controller access When you create a GKE private cluster with a private cluster controller endpoint, the cluster's controller node is inaccessible from the public internet, but it needs to be accessible for administration. By default, clusters can access the controller through its private endpoint, and authorized networks can be defined within the VPC network. To access the controller from on-premises or another VPC network, however, requires additional steps. This is because the VPC network that hosts the controller is owned by Google and cannot be accessed from resources connected through another VPC network peering connection, Cloud VPN or Cloud Interconnect. https://cloud.google.com/solutions/creating-kubernetes-engine-private-clusters-with-net-proxies