Daughters new iPhone says no backup found on icloud

Syncing content such as Photos and Contacts is not the same as actually backing up the phone.

On your daughters iPhone open the Settings app. Tap Her name at the top. Then tap iCloud. Make sure iCloud Backup it turned on. Make sure Back Up This iPhone is turned on for Automatic Backups. Then tap Backup Now to ensure she has a current backup.

Making sure these settings are turned on, will ensure the phone backups automatically at night, when the phone is plugged in to charge and connected to Wifi.

You could try to sign out of iCloud entirely and restart your iPhone by turning it off and on. Then, sign back into iCloud and attempt to back up or restore again.