Thanks to the recent development of React Native which includes Babel 7, it became really straight forward:

npx react-native init MyApp --template react-native-template-typescript

When finished we can already start developing. Debugging works as well. Here’s a demonstration of working breakpoints in Visual Studio Code:

So you can now start working on your app, just like you are used to but with TypeScript.

The TypeScript template is an MIT licensed open source project: https://github.com/emin93/react-native-template-typescript