Oh they very much can.

When I was a kid, ours opened the doors by jumping at the door handles. Grabbing them and pulling them down.

They even taught their kittens

We had to install all handles so they pointed upwards, just so the cats couldn't grab them

But even that only lasted a couple months until they learned to latch onto them anyway and wiggle around until their weight pulled the handle to the side and opened the door

Clever fluffy bastards