Feeding vertex data to a compute shader
You will need a new chunk of memory for the new surface anyway, so why not read from the original and store directly in the result.

Having precomputed normals will reduce a lot of the computation requirements though (especially needing to find&amp;read each neighbour), the user action of the extrusion will probably be interactive so you will have multiple frames with different extrusion amounts but the normals of the original surface won't change. Having the normals be around will likely be helpful for other operations as well. You could make the temporary transformed geometry just a vertex shader trick as well and only commit the result once needed.

Computing normals is much simpler by going face per face and then summing the the non-normalized normals per vertex and normalizing after.