How do I get my software update to work when it is stuck on estimating time remaining

VPN or proxy connections might prevent your device from contacting the update servers.

Get help with over-the-air iOS updates - Apple Support

Remove and download the iOS update again

If you still can't install the latest version of iOS, try downloading the update again:

1. Go to Settings > General > [Device name] Storage.
2. Find the iOS update in the list of apps.
3. Tap the iOS update, then tap Delete Update.
4. Go to Settings > General > Software Update and download the latest iOS update.

If you don’t see the update in the list of apps or if the issue happens again, you need to update your device with iTunes.

Get help with iOS update and restore errors - Apple Support

If you see an error when you update or restore your iPhone, iPad