Is it possible to backup without root?
adb backup should work at least on some apps. Test it for example with a simple tea timer or stopwatch app those apps should not disallow backup. If this does not work the backup function on your device may be defect (encountered this once on a Lenovo tablet). 

But if it works for simple apps that the it is just that the other apps disallow backup (android:allowBackup=false set in AndroidManifest.xml). Note that this settings affects disables adb backup as well as Google Cloud backup.

If the app disallows backup then there is other way to backup the data except using root permissions.

However if you have root and TWRP installed you may be able to perform a user data backup. However AFAIK this only works if TWRP is able to decrypt the user data. If you only see the encrypted files or the encrypted partition I doubt that restoring those files will later work on the same device (it will never work on a different device).

Note that a (decrypted) user data backup independently how it was created can not be directly restored via ´adb push`. For doing so adb would have to run with root permissions which is usually no longer possible (unless you have a manipulated adb version on the device). 

What you can do with root permissions is backup and restore app user data. For example manually by using tar in an adb shell with root permissions.