Extrude the edges shown in green inwards a little to create the polys in red and give this area a nice lip.
We need to put the door cushion over the hole in the door. To start the cushion, first create a poly with 3 width segs and align it with the bottom of the door as shown by the polygon outlined in green. Now it's just a matter of extrudes upwards as shown by the red arrows.
Now give the cushion some depth by extruding the outer edges into the door. Select the edges shown in green all around the cushion except the top and extrude them to create the red polys.
Adjust the shape at the top of the cushion to be more like the picture.
From the back of the cushion, select the edges shown in green and extrude them inwards as shown. Make sure to weld any vertices that need welding.
Time to do some chamfering to sharpen edges. Chamfer the edges shown in green. There are a few edges not shown in the picture that you must also chamfer and it should be obvious which edges they are. I chamfered by a value of 0.7 but you can experiment with the values. That's all for the door cushion for now.