2.3 TB ~= 4* 512 GB.
Suffice it to say the whole thing won't fit.
Unless you know which archives you no longer need, restoring the whole backup is not going to be practical on a 512 GB machine.
It may be possible while time machine is off to use the Finder or Shirt Pocket Superduper to copy over folders to a different drive that you don't mind cherry picking a recovery, and only recovering some more recent one as part of the move.
Use the Finder's File menu -> Get Info after clicking once on various backup folders to get an idea where you can save space on the recovery.
In the end you don't want to add to the recovery more information than it would take to fill up more than 85% of the destination drive. If the destination drive only has an operating system, once you have paired down your backup, you could even save a little more space by wiping and reinstalling that operating system and using the setup assistant to bring over the time machine backup of choice. Otherwise you will have to spend extra space merging users through the Users-> Shared folder to make sure you don't overwrite data already on your destination drive.