depends on phone manufacturer and model.
parts of your data is stored in a root partition, and without being rooted you cant access it
and rooting a phone might clear the memory and thus nothing will be accessible
one way would be to desolder the "flash" and read it, but if this is encrypted you will be out of luck
there might be a specific software/app that can read rooted info to make a backup of it ie messenger backup or some
other software
this depends if you want to recover all or just some of it.
this sound easier than it is in reality
there are lots of reason that data is stored in a root partition like digital certificates or encryption keys.
i hope this can get some ot it answered.
regards sphinxios