This is the same problem which was created for me. A person installed a new flange, new toilet and new floor. One of my screws go into the joist and the others go into the air space and dangle. How nice. I had an access panel put in underneath and can see them.
Another person came in ( when I requested the floor to be fixed correctly) and threw down 1/4 inch Luann board which sure, covers the gap but, a screw cannot bite into 1/4 Luann board and in time will warp and rot.
I am not a plumber but, if I were you, I would replace that floor where the gap is at and make it a nice, sturdy floor to work with. That is what I intend on doing. Myself. So far as the others, I sued them, if only they would had cooperated.
You can try to put boards up underneath if you can, but seriously, I don't think that is good either.