As best place and practice for external API calls is React Lifecycle method componentDidMount(), where after the execution of the API call you should update the local state to be triggered new render() method call, then the changes in the updated local state will be applied on the component view.
As other option for initial external data source call in React is pointed the constructor() method of the class. The constructor is the first method executed on initialization of the component object instance. You could see this approach in the documentation examples for Higher-Order Components.
The method componentWillMount() and UNSAFE_componentWillMount() should not be used for external API calls, because they are intended to be deprecated. Here you could see common reasons, why this method will be deprecated.
Anyway you must never use render() method or method directly called from render() as a point for external API call. If you do this your application will be blocked.