How can I convert a low resolution image to a mesh? I have a low resolution Image I want to recreate as a 3D object. I was thinking of making 7 separate "layers" to depict foreground and background elements. Basically, once the layers were complete they would stack to create a 3D picture. Each layer would have its own textured color. I would combine them at different depths.

I am bit unsure how to proceed with the process of this. Would it be best to create each layer, extrude to the right depth and then snap them together and join them into a single object? The idea is to 3D print this as a personal project. Reference is attached.
Maybe you should model the whole scene (make some quick low-poly models) and then use the Remesh Modifier. Set its mode to Blocks. Apply the modifier and then paint the model.