How to anchor floating toilet flange
If your subfloor is questionable, you should tear up the section surrounding the flange, between the joists, then block between the joists on either side (or front and back, depending on orientation) of the flange, and replace the subfloor material.  Then you can screw the flange to the new subfloor, with a spacer or shims.
You don't need the CBU or tile to fit under the flange.