Create SSO user using the API

I currently have multiple enterprise connections and a single database connection setup for authentication purposes. In our app, when we create a user, I call the create user API endpoint and create a user in the database connector, this is fine for DB connection users.

For our enterprise users, instead we go through a convoluted process of getting the user to sign in, which creates a default user in the enterprise connection, then manually in the Auth0 UI, update the user with our internal set of claims. So my questions are:

  1. How do I use the API to create an enterprise user in Auth0?
  2. How do I stop Auth0 automatically creating enterprise users, i.e. I only want users being created via the API call, not by trying and failing to sign in?