Laser is used to cut different materials (wood, cork, acrylic plastic, leather, cloth, felt, card, paper, etc), normally flat. But not all them have to be the same thickness. It can also engrave the surface, but not raise it. It can affect the edges, but the rest is left as it was.
You can already buy some examples, from simple street maps where building blocks are removed so you get a web of streets, to more complex maps with multiple height levels by stacking layers of materials to form the surface and combining different types and colors (useless for you) to add more information.
It would be similar to what you have been getting done by hand.