GKE does not scale to/from 0 when autoscaling enabled

Update:

Note: Beginning with Kubernetes version 1.7, you can specify a minimum size of zero for your node pool. This allows your node pool to scale down completely if the instances within aren't required to run your workloads.

https://cloud.google.com/kubernetes-engine/docs/concepts/cluster-autoscaler

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Old answer:

Scaling the entire cluster to 0 is not supported, because you always need at least one node for system pods:

See docs

You could create one node pool with a small machine for system pods, and an additional node pool with a big machine where you would run your workload. This way the second node pool can scale down to 0 and you still have space to run the system pods.

After attempting, @xEc mentions: Also note that there are scenarios in which my node pool wouldn't scale, like if I created the pool with an initial size of 0 instead of 1.

Initial suggestion:

Perhaps you could run a micro VM, with cron to scale the cluster up, submit a Job (instead of CronJob), wait for it to finish and then scale it back down to 0?