Private Google Access is a specific feature designed for this exact scenario. When enabled on a subnet, it allows virtual machine instances (including GKE nodes) that only have internal IP addresses to reach the public IP addresses of Google APIs and services. This communication stays entirely within Google's network, ensuring that traffic does not traverse the public internet. This configuration directly meets the requirements of accessing Google services securely without assigning external IP addresses to the cluster nodes.

A. This option directly violates the core requirements of the question, which are to avoid using external IP addresses and not traverse the public internet.

B. Cloud VPN is used to connect a VPC network to an on-premises network or another VPC. Configuring it back to the same VPC is not a valid or functional solution for this use case.

D. VPC Service Controls creates a security perimeter to prevent data exfiltration from Google Cloud services. While it enhances security, it does not provide the underlying network path for private connectivity.

1. Google Cloud Documentation, "Private Google Access overview": "With Private Google Access, VMs that don't have external IP addresses can reach the external IP addresses of Google APIs and services. ... Traffic from a VM in a VPC network to Google APIs and services stays within Google's network."

Source: Google Cloud Documentation, cloud.google.com/vpc/docs/private-google-access.

2. Google Cloud Documentation, "Private clusters concepts": "Private Google Access provides nodes with private IP addresses access to most Google Cloud APIs and services without requiring an external IP address. For example, your cluster needs Private Google Access to pull images from Artifact Registry or Container Registry."

Source: Google Cloud Documentation, cloud.google.com/kubernetes-engine/docs/concepts/private-cluster-concept. Section: "Access to Google Cloud APIs and services".

3. Google Cloud Documentation, "VPC Service Controls overview": "VPC Service Controls helps you mitigate the risk of data exfiltration from your Google Cloud services... You can use VPC Service Controls to create perimeters that protect the resources and data of services that you explicitly specify."

Source: Google Cloud Documentation, cloud.google.com/vpc-service-controls/docs/overview. This reference clarifies that VPC-SC is for data exfiltration, not connectivity.