C4D lite comes with your After effects subscription. you could definitely create this very easily with C4D lite and have this as a C4D layer in Ae with textures, lights and what not. here's a very nice free course (only need to register) about it:
and you could do this with After effects but it will take a while to setup and you won't have too much flexibility with the appearance of your 3d box (the edges for example). you would need create the rectangle out of 6 solids layers, essentially making a paper box out of 6 papers. align them properly in 3d space, then replace the solids with a texture. here's an oldie but probably good because it's from creativecow:
Other than Roei's tutorial link, this is pretty easy to follow along too and it uses AE's Snapping feature to more easily create 3D boxes or other well-aligned objects.
To snap your image onto a side of the box, you will want to use the Shift+Parent feature. However, ensure your rectangle's Scale is at 100% for its X,Y and Z values. Otherwise, the Shift+Parent routine will distort your image as the Shift+Parent routine forces your image into adopting the Scale values of the source (snapped to) layer.
Taking a look at that course now.
I was able to use AE to create a pseudo 3D product box by following along on how to make a 3D cube on Youtube. 6 images, 3D layers, moved and rotated to mock-up a product box. Looks ok. Added some lights and a camera, and am kind of able to do what I want. The edges are unaliased and jagged, and the animation is clunky to me. But it essentially provided me with what I'm trying to accomplish.
However, I just signed up for that course and I'm going to try and see what it can do. I had no idea C4D Lite was available to me and it looks like it's worth investing a little time into, not just to create my product box animation I'm trying to do, but looks like it'll give me so many other options to explore in my videos as well.
I cannot tell you how much I appreciate your response. Perfect.