If it's a brand new device you will have free phone support for 90 days. This may be something you want to talk to Apple about. But I see two options for you: walking through the above steps, or completely erase your phone and starting over using the same backup in iCloud.
That being said, I feel like you can still perform the above steps, but turning off iCloud backups deletes the backup from iCloud. I recommended hooking it up to iTunes so you have a backup somewhere. You can still do the aforementioned steps but if you leave out the iTunes part, you will not have a backup anywhere unless you have previously hooked it up to iTunes.
Here's what would happen when you turn off iCloud backups; it deletes the backup from iCloud but does not remove anything from your iPhone. So once you turn iCloud backups back on, iCloud acts as if it has never had a backup of your phone and thus starts a new one. If you decide to go forward with the steps, make sure you are on a strong and reliable wifi. This link will walk you through deleting your iCloud backups. Look at the section, "Delete backups and turn off Backup for your device." Once that's done you just turn iCloud backup back on and select what you want to back up.
https://support.apple.com/en-us/HT204247
The other option I see, is completely erasing all of your data, and setting it up again the same way you did the first time. This sounds scary but is actually pretty simple. Something obviously went south the first time around so it may be easier to just delete everything and restore from the backup a second time. Again, you have to make sure you have a good, uninterrupted network connection since a bad connection is usually what causes a bad restore via wifi.
iCloud: Restore or set up your iOS device from iCloud
Either way, I don't see you losing any data, and honestly, I think deleting your content and simply restoring again would be the best way to go since you know iCloud has a backup of your device already. It will take longer than turning iCloud backups off and on again but given your circumstances, it is likely the most reliable way to do this.
