It seems that the best available option that you might try - because it doesn't seem to have an official way to do it - it's by using API keys to perform the verification and security of your calls. As clarified in the official documentation Using API Keys, this is not supported by all Google applications, but Cloud Endpoints should work.
Considering that, you can use Cloud Endpoints in integration with your Cloud Functions, to provide security via API keys. You can find more information on how to achieve that in this article here.
Another alternative you may want to try, it's using a JWT token - as clarified here - as a header in your API calls. This way, you will be working with authetnication via keys - not exactly as in AWS, but it's a start - so you can secure your calls. :)
Anyway, if you don't find this useful, I would recommend you to raise a Feature Request in Google's Feature Tracker, so they can check about the possibility of further implementation in such functionality.
Let me know if the information helped you!