Topology Circluar Quads I can't seem to wrap my head around on how to make a cricle from a square in a nondestructive way.

The result I'm trying to achieve is this:


Starting from this:



I've tried inserting a face but it won't let me slide it anywhere from it's starting point. I've also tried extruding and then scaling it in but the shading gets all weird. I just want to add the extra edges and make it more like a circle.

Any help would be appricated!
Inset the faces with I, then use To Sphere tool (Shift+Alt+S,1) to make the edge loops round.


Next enable the proportional editing (with a Sphere falloff type) and transform the middle vertex upwards (G,Z). Finally extrude the four middle faces upwards (E,Z).