Are you running the service as a Web Service or a Static Site? For basic React apps we typically recommend a Static Site, per our doc example: https://docs.render.com/deploy-create-react-app.
If you wish to use a library that cedes routing to your application you will need to run it as a Web Service so your routes get properly processed on the backend.
Hope that helps!
Regards,
Mike
Render Support Engineer, MT (UTC-6, UTC-7 in Winter)