I am away from my workstation so the tab locations are from memory…, but I think the first part might be to try and achieve the basic structure of the shape, then you can pursue the scaling/attraction to a logo/image.
The first part looks a lot like a triangular mesh. Try making some random 2d points, (vector tab), then make a delunay mesh, (mesh tab). Then get the face boundaries, (mesh tab), and fillet those, (curve tab). You could then get the center point of those faces, (mesh tab…or use the area from the surface tab…it will work on curves as well), and move them up some distance, (vector tab, z vector to describe distance “up”, and transform tab->move). Once you move the curve up, (by describing a translation vector), you could scale those “upper curves” down some amount. Lastly, you would loft the original filleted face boundary and the translated boundaries, (the ones you moved up). This would result in a cone like surface that could be unrolled. I would bet that all of those parts in the image you referenced are cones, (which means that instead of lofting curves, you should extrude point(Surface tab…I think). Then they literally “pushed” the cone tips in to get the hole.
You mentioned that you were new to GH, so I would suggest starting with something like I described. I apologize in advance, as I did not look at your definition, but if you have something close, maybe we can take a look tomorrow and put a few starting points together.