Here is a good way. Get some plywood the same thickness as the old stuff. Cut out a nice neat patch. Lay the patch on the floor and cut the old floor to match. Use a router to rout a step in the floor and in the patch so they overlap. Put the patch in with wood glue and screws for a permanent repair.
This is too obvious but you have to measure back from the traced outline, before you cut, to leave enough material to overlap.
Living in the trailer park of sense, looking out the window at a tornado of stupidity.