How do I autostart Jenkins agent machines?
We use AWS's EC2 Plugin to spin up spot instances in AWS for our Jenkins master based on a single AMI, exactly as you describe, so Jenkins does support this behavior.

From a quick bit of searching Google Cloud seems to offer a similar solution; 


  Spotinst’s Jenkins Plugin helps you to do more with your Jenkins setup by allowing you to automatically configure and scale a designated Google Compute Engine Preemptible VM as Slaves up and down depending on the number jobs to be completed.