You could boot the system using a Windows 10 installation media flash drive.
When the "Windows Setup" screen appears press Shift + F10 keys on the keyboard to open a command prompt window.
In Command Prompt type notepad.exe and hit enter.
In Notepad, click File, then Open. Now you will have Explorer window that you can use to locate folders files that you can save to an external USB disk.
You won't see a progress bar while copying and it will appear to be frozen...just be patient and wait for the files to finished copying.
You can use the same Windows 10 installation media flash drive if you have one with enough space.
Make sure to always leave at least 12% available space.
Also, you could removed the disk, connected to another computer and create some space by removing files.
If after creating space is still stuck, go back to command prompt, navigate to C:\Windows\SoftwareDistribution and delete the content of that folder.