I'm on a Macbook Pro, Mojave version 10.14.6. Running Illustrator CC 2020, version 24.0.3.
When I click "Create new" from the start screen, nothing happens. No error message, just ... nothing happens. I can click "Open," and open an existing document. I can double-click on the template options and create a new file that way. But "Create new" button doesn't work.
I have already deleted caches and preferences in /Library/Application Support/Adobe/, /Library/Caches, and /Library/Preferences. I have already tried uninstalling and reinstalling.
Sorry to hear about your experience. I'd recommend contacting Adobe live support via chat on https://helpx.adobe.com/support.html Click on chat icon at bottom right corner to begin conversation. Support theam there will be able to perform remote troubleshooting on your machine and help you out accordingly. Hope it helps.