* Set an autoscaling group with your instance template, max instances 1, min instances 0, desired instances 0 (nothing is running).
* Set up a Lambda function that sets the autoscaling group desired instances to 1.
* Link that function to an API Gateway call, give it an auth key, etc.
* From any machine you have, set up your cron with a random sleep and a curl call to the API.
And that should do the trick, I think.
You might as well just call the ASG API directly.
* Set an autoscaling group with your instance template, max instances 1, min instances 0, desired instances 0 (nothing is running).
* Set up a Lambda function that sets the autoscaling group desired instances to 1.
* Link that function to an API Gateway call, give it an auth key, etc.
* From any machine you have, set up your cron with a random sleep and a curl call to the API.
And that should do the trick, I think.