Quick start - Software update stuck at first activation of the phone

I bought a new iPhone 14 and wanted to transfer all the data from my previous iPhone XS via Quick start. It was a MUST for me to use this native feature of Apple, instead of using third party apps or cables and iTunes. But it turned out that in my case, experience was awful, and this feature was completely not in the Apple philosophy, to keep things simple.

Problem: to reach the step of transferring the data from one iPhone to another, your new phone must have the latest iOS. In my case, new iPhone 14 had the iOS 16.6 out of the box, and my previous XS had iOS 17.0.2. After configuring Face ID, I had to update the iOS. But it couldn't do it! After downloading and preparing the build, each time I pressed "Install now", as if something has started but nothing would happen. Even after 3 hours, no progress was made. I tried 3-4 times - no result. My wife also has a new iPhone 14 and I tried the same on her phone (Quick start > Transfer data) and again the same problem with software update. It didn't work even if I select the option to download from iCloud, in that case a received error that "No back-up is available for this iOS version", also need to to have 17.0.2.

Workaround: I used the option to start using the phone without transferring any data. Logged in with my Apple ID. In this case, it doesn't require to have the latest iOS. After configuring the phone, I accessed Settings, and made manually the updates (first the iOS 16.7 and after the iOS 17.0.2). After that I erased all the content and reseted the iPhone and start the process again, with Quick start. IT WORKED! It didn't have to update the software anymore, so I easily reached the "Transfer data from iPhone to iPhone", as it should be.

I hope someone from Apple will read this post and make changes to the mentioned process. Or, at least, will include some exact instructions, what user needs to do. Because honestly, I was thinking to bring back the device and get back the money. I was very frustrated. And such solution I couldn't find on the internet.

All the best!