is there a way to keep extruded faces smooth so you can animate them out of nowhere?

Take for instance when you click on a face and simply press e, then right click. You’ve just extruded a face that is perfectly overlapping with itself. However, if you tried that on a larger mesh that you subdivided or applied smooth shading too, even though those faces aren’t yet extruded, you’d notice the mesh seems cut around the edges of those faces. However, what I want is to eventually animate those faces so that those extruded faces perfectly blend into the mesh, but then emerge and create a new extruded shape out of the surface.

B…

Yeah, bake an object space normal map from the base shape, to the shape with the extrusions added. Then use a shape key to animate the extrusion, and set a driver on the normal map strength that is keyed to (shapekey.value == 0.0) It’s pretty straight forward.