When my four cats were still young kittens (just a few weeks old) I blocked up the cat gap (which should have been a cat flap but the actual flap was missing) with some very stout cardboard. However their mother was determined to show them what lay outside and managed to rip it open.
So I got a sheet of extra thick cardboard and layered it on both sides with double-strength cloth tape (which normal scissors wouldn't cut through - I had to use extra big ones). Then I repeated the job, so that I'd got two heavily reinforced pieces of really thick cardboard, which I put one on top of the other, joining them with yet more of the cloth tape. I then fixed the doubled-up (and super-strengthened) cardboard over the gap, securing it with several layers of the strong tape.
Knowing that I'd created an obstruction that it would be hard to penetrate with a power drill, I then went out to the pub. When I came home there where four tiny kittens in the street, being carefully shepherded around by their proud mum. She'd totally shredded the 'impenetrable' obstruction in her path!