You can try using the web service called Codemagic. It allows you to build an .ipa file from a React Native project. However, you will still need a developer account to run the .ipa file with TestFlight.

This video demonstrates how someone built a Flutter app into an .ipa file, and the process should also work for React Native. The video also shows an alternative method using AltStore to sideload the app onto the phone without using TestFlight.
https://youtu.be/m3_6z2wfHiY?si=o5xginYzHxmL0C-t