Actually i was thinking about it a little more and this idea isn't completely crazy.
what if, say fred invented some kind of compression machine that pushes down on a square from all 4 sides and is completely sealed off so that not even a single atom from the square would be able to escape. It pushes down on the square with such extream force that it starts to get smaller just by the atoms trying to fit closer together. If he keeps adding force the atoms would get so tight together they had nowhere else to go but after a certain point all the atoms wouldn't be able to get any closer together but still more force is being added so they would eventually have to go somewhere. Its possible they could bend out into a 3rd dimension as the only solution.
even if this method was possible though fred wouldn't be able to see the 3 dimensional figure he created since he is still 2d himself. so if we somehow did this on a cube in the 3rd dimension we wouldn't be able to tell if it worked or not either, and we couldn't put a person into it hoping to make him 4d so he can tell us if it worked because he would die long before the process finished
this is all speculation though because the kind of force I'm talking about couldn't be realistically achieved, at least not with our modern technology. Think this could possibly work though?