Software verification process is Apple server based and can take a while. Shouldn't be more than 15 minute, 20 tops. I would give it 30 and go do something else. If its taking hours then try again later...
However being the integrity of the software is being checked via Apple servers....
Make sure the device is plugged in with strong wifi connection. Make sure something else is completely saturating your network like 4k Netflix in multiple rooms or updating 10 Apple devices at the same time.
Make sure you aren't using a VPN (it will work however its not doing you any favors for this task)
Close all other process. Reset the device.
Delete the iOS update and redownload it.
Try again later. A single drop in the network between your iPhone and Apple and that verification will likely fail.
Where I live Wifi channels can get spotty, if I'm doing a mission critical task I'll power cycle the router so it connects to a channel with the least amount of people.
Use iTunes from a Mac/PC.
Hopefully by the time you guys read this its from an updated iOS device.