No need to use any template here. Just create a blank install with your desired install name.
After you have recieved confirmation from WP Engine that your install has finished setting up, create a new repo using this template.
It is important that your repository name matches your WP Engine install name, as it will be used for directly establishing a connection with the install using the wp-engine workflow.
There is a helper action working to add some aditional files to the repository. Give this a minute to finish. You should see a new commit from @designcontainer-bot when the workflow has finished.