Deleting files (and emptying trash) does not change amount of drive space that is "Used".
I have a 1TB internal drive. The finder reports that there are 504GB used on this drive. I would like to make a Time Machine back up of all of this to an external drive. However, the external drive is only 500GB. No problem, I thought, I'll just find 4 or 5GB worth of cruft to delete and then I'll have room (note, this is for a one-time offsite backup and I only need the initial time machine snap shots, so having extra room for subsequent delta backups is not relevant here).
As luck would have it, I actually found about 30GB of files that could safely be deleted. I put them in the trash, emptied the trash and restarted the machine. Now the finder reports that I have about an additional 30GB of space "Available", as expected. However, the amount of space that is "Used" is reported as having gone up slightly, rather than down by about 30GB, with the result that Time Machine still complains that there is not enough free space to complete a backup.
So what gives? How does one actually get the "Used" number to go down if deleting files won't do that?
Mac mini, macOS 10.14