No permission to create an App Engine application

You need this permission:

appengine.applications.create

If you try to create an appit within the console:
~ $ gcloud app create

you will get exactly the this permission role missing but incredibly this permission is not assigned by default to the administrator. Thus, either create a new Role with this permission or just add this permissions to any role you already have

You probably have an IAM role on the project that doesn't include access to App Engine.

https://cloud.google.com/iam/docs/understanding-roles

You can ask the project owner what role you have on the project (unless you are a project Owner, Editor or Viewer, in which case you can see your role on the Permissions page).

I also got this error. It seems you need to be Project Owner to be able to create App Engine applications.