How to incorporate color into art work

Does anyone know how I can paint a surface and then engrave over it. I have been asked to create something similar to the picture I’ve attached. I already have the disc and the head in a program. Any thoughts would be greatly appreciated as always.

A couple approaches I have applied:

With the example you have illustrated, the silhouette aspect of the piece makes for an ideal opportunity to pre-paint the yellow / red background on the material first. Let that dry / cure. Then laser engrave the dinosaur skeleton and black box.

Thank you as always. Appreciate your help.