It is all about the motion of the tectonic plates. NA is moving SW and has for tens of millions of years. But guessing 30 million years ago is when it passed its "closest to the pole" point and, as is motion on the surface of a sphere, started to move away. The angle of the fault at the bottom of the center of the North Atlantic is the key. That has been pushing Greenland NW and Europe SE for over 100 million years. Greenland is where NA was 40 million or so years ago, same arc.
So, NA moved north, got within 600 miles of the North Pole, started to stack ice, grew its continent specific ice age, and then moved away from the pole and the ice age ended because it melted.
These maps show the extent of the "North American Ice Age," but are wrong because they have Greenland frozen too and we know Greenland was GREEN 1 million years ago...