"Injecting" configuration into a create-react-app is done with environmental variables. I always have at least one for the root of my REST API or GraphQL endpoint.
When running in development, I set that variable to point at a local version of the backend server I have running on my laptop. That's some other project that I do whatever I need to in order to get it running and available to accept requests from my React app.
If I wanted to start simple with static JSON files, maybe I would use something