while you could probably fake this to some extent in 2D animation, judging by the lighting and material and shadows and organic curvature of the pixels (something that is especially difficult in Ae) - this was probably done in a dedicated 3d application.
So that means the limited 3D workspace in after effects couldn't do that?
Doing that in AE would require a 3rd party plug-in like Element 3D or Zaxerks or Forge Freeform PRO, or maybe even Boris FX and a bunch of fiddling around and probably several hours of experimentation. Nothing is moving in that shot so it would be doable, just not automatic.
C4D lite, included with current AE Subscriptions is not up to that task. You could do something like that in Blender (open source and free at blender.org) or any other 3D app if you had some modest modeling and animating skills. I would start with at the end, make the logo a separate mesh, then animate the mesh away from the cup. Pretty simple standard 3D techniques here. The hardest part of the whole project would probably be the texturing to get everything looking photographic....
If I were stuck with AE I would carefully shoot footage then probably use FreeForm and some displacement to fly the logo in and attach it to the cup. Might model the displacement map in C4D Lite, but probably would use Blender to pull it off. If my shot involved a moving camera I'd probably do everything but the final composite in a 3D app.