It's not just the screen that's broken, if you've rebooted the phone at least once before trying to recover files, it appears that there's no OS in the phone. Your pictures may be in there, but since you can't boot a boot.img file, you can't find out.
Check on
Google Photos to see if your pictures are backed up. If they are, you can either download them, or just put the same Google account into a new phone and they'll sync.
And no, you can't use Odin to enable debugging. Debugging is in the Android partition, not the bootloader partition (which is really what "Download mode" is).