To use a Virtual Private Network (VPN) to connect to an instance without an external IP address, you must have a computer that's already connected to the same VPN as the instance you want to reach. For example, you might have a VPN that your local on-premises network shares with your GCP VPC.
Connect to an instance without an external IP address by using the gcloud compute ssh command with the --internal-ip flag.
gcloud compute ssh [INTERNAL_INSTANCE_NAME] --internal-ip
Where [INTERNAL_INSTANCE_NAME] is the name of the instance that you want to connect to.
After connecting, run commands on your instance using this terminal. When you have finished using the instance, disconnect from it by using the exit command.