How to I restore my new iPhone after it is set up?

I switched carriers (from Sprint to T-Mobile) and kept the same IPhone model just different phones (iPhone 6s). I understand that it gives you the option when you re setting the phone up initially with the basic prompts to set up as new phone or restore using iCloud backup. The thing is, I'm not able to choose the iPhone backup I already have saved because it needs iOS 9.2 or higher. This can't be accomplished until after I set up the phone and can choose to do the software update from the iOS 9.1 to 9.2. I tried resetting my phone already and it always gives me the same prompt (backup requires iOS 9.2 or higher).

My phone is set up as a new phone, but I want to restore it using iCloud backup.

Just set it up without a backup, upgrade it to 9.2, then reset it and set it up again, this time restoring from the backup.

You can follow these steps:
1. When set up your iPhone, select Set Up as New iPhone on the Apps & Data screen.
2. Follow the remaining set up process, you can skip the steps for Apple ID and passcode.
3.Once the set up is done, update your device to the latest version of iOS software.
a. Plug your iPhone into power and connect to the internet with Wi-Fi.
b. Tap Settings - General - Software Update.
c. Hit Download and Install.
d. To update immediately, tap Install.
4. After the update is finished, your iPhone will restart.
5. Tap Settings - General - Reset - Erase All Content and Settings. This will reset your iPhone again. Now you are able to set up your iPohne with a iCloud backup