While you can't import Objective-C headers directly in Swift files, you can import them all into a bridging header file, which will subsequently be exposed to your Swift environment throughout the project.
Thus, you should write into the bridging header the union of all headers you'll be referring to (e.g. due to invoking APIs or asserting types) in your Swift code.
For a React Native project, the fundamental headers you'll need come from the React
static library. If you call upon any native modules, you'll need to import their headers, too.