At the moment, you need outbound internet access to interact with other Google services from a GCE instance. There are several ways to achieve outbound internet connectivity from an instance:
1) Use an instance with a public IP address. You can configure the instance to reject all incoming traffic by ensuring that there are no firewall rules that allow traffic to that instance.
2) Use another instance as an explicit proxy. You can either use a SOCKS5 or an HTTP proxy; in either case, you'll need to make explicit configuration changes to the machine with the private IP address, as well as installing software on the proxy machine. Here is an example for setting up an HTTP proxy:
3) Use another instance as a transparent proxy (via NAT or VPN to your corporate network, for example). The benefit of using a transparent proxy is that you don't need to make any configuration changes to the machine with the private IP address. The disadvantage is that it can sometimes be harder to troubleshoot problems if they occur. Here is documentation for setting up a transparent proxy: