I downloaded the images of all box six sides from the URL in the description. I inverted the colors, traced the vectors in Inscape and extruded the STL model in Blender.
I had problems with scale as I did not use any 3D program before but I scale the model in a printing application (maybe you will need to do the same).
I printed each side in 78 x 78 x 0.5 mm dimensions to match the size of the wooden cube I prepared. I cut it from 78 x 78 x 500 I bought in the local hardware store.
The models were printed on Be3D DeeGreen printer on high settings and most of them in 60% speed (few of them in 100%).
The sides were then painted with gold metallic color used for plastic models and glued to the sides of the painted wooden cube. The whole puzzle box is lacquered to get a nice shiny look similar to the one in the movies.
This is just a first prototype. The next time I will use better wooden cube (unfortunately not all sides have the same size), more precise print settings and better coloring for a more polished result. I will update the photos when I will have another version.