How do I fix iPhone 16e setup getting stuck at iOS 26.2 update?

Force-restart it:

1. Press and quickly release the volume up button.
2. Press and quickly release the volume down button.
3. Press and hold the side button until you see the Apple logo (this might take longer than 10 seconds).

The operative word here is QUICKLY for the first two buttons, then a long hold for the SIDE button; and try it a couple of times, the timing is a little tricky.

If it doesn’t start with the Hello screen reset it to factory settings: Restore your iOS device to factory settings - Apple Support

When you have the Hello screen start the setup again, then set it up as new, without syncing or restoring and skip over every option until you get to the Home screen. Then go to Settings/General/Software Update and update it.

Finally, restore to factory settings again and do a normal setup.

You can get into your new iPhone without pairing it with your old phone. If that were not the case no one could ever be a first-time iPhone user. So for the moment pretend you are a first time user. Turn off your old phone so it doesn’t interfere. Set it up as if you never had an iPhone before, update it, then reset it and start over pairing it with your old phone.

"How do I fix iPhone 16e setup getting stuck at iOS 26.2 update?: bought new iPhone16e. Cannot set it up as it it keeps getting stuck at the Software Update IOS 26.2 screen."

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iPhone Stuck At an Update:

So, is it rebooting? Or is is just stalled? Either way, see if this fixes your issue: How to Fix an iPhone in a Boot Loop - Apple Community