Thank you all for the advice. Unfortunately, my intention is to fold the cardboard into a cardboard box during animation during close-ups of the camera. The plane must be rigged and the edge of the cardboard look photo realistic and unfortunately in high resolution
Single face displacement will only get you so far.
Just to illustrate.
Single face displacement
The image texture is used to "extrude" the original face.
Notice the incomplete rims, rough appearance, and high required geometry.
Faces: 1 000 000
Three faces on top of each other.
Displacement is used on the middle face only, to creating the ...
I would make the squiggle with a separate mesh in between the two side planes. If you do still want to use the displacement modifier, you will need to use more subdivisions or a higher resolution mesh. Hope this helps.
"I'm trying to map a texture to a cube"
Perhaps a simpler way of mapping a texture to a cube and have control of the orientation of the texture on each of the 6 faces is to use UV mapping?
Starting with the node setup you have already :
In the Texture Coordinate node change to UV, and the Mapping node change to Point (and reset the rotation and scale to ...