I spoke too soon. The deploy will bring up an instance instead of your first request. To force a cold start, you could set concurrency to '1' and send two concurrent requests. You should see a log entry such as the following when a new instance starts up:
"This request caused a new container instance to be started and may thus take longer and use more CPU than a typical request."
Alternatively, you could set up an endpoint that shuts down the server (which will shut down the instance - not advised for production code).
As an aside, the "K_REVISION" environment variable is set to the current revision. You can log or return this value to test whether traffic has migrated to a new version (instead of waiting a minute).
I'd encourage you to test your particular app, but you should expect similar cold start times in Cloud Run.
You can set "Maximum Requests per Container" on container deployment so you are in control whether a container has single concurrency (i.e. "Maximum Requests per Container = 1"). If your app is not CPU-bound and you allow multiple concurrent requests (the default) you should see fewer cold starts.
As an aside, the "K_REVISION" environment variable is set to the current revision. You can log or return this value to test whether traffic has migrated to a new version (instead of waiting a minute).