are you going for cheesy popout effects also known as 2.5D? Think background rotates faster than forground.
AE does have a free displacement matte plugin, coupled with a depth matte(you can hand draw or key), you can create psuedo 3- d distort effects like in film chronacles of narnia 2d to 3d conversion.
Anything more than that, you’re looking at manual labor involving digital matte paintings and hundreds of artists and thousands of hours.