I was able to get in by doing these. Not sure if these are necessary:

- Go to instagram app on the App Store. Scroll down to the section where it says other apps from the same developer. There, next to the Threads app, I had the download button. After installing the app I still was not able to open it.

- Once I had the app installed, I clicked through (on twitter) on someone's threads.net link and that kicked off the initial setup of the Threads app for me.