Zoom in on a section and then draw in a bit of geometry to measure the thickness of things:

then delete the drawn piece and select the geometry and inset the path by an appropriate dimension:

and repeat:

Then draw in additional geometry:

Note that since this is symmetrical you can duplicate and flip geometry and reposition it rather than drawing elements twice.

Select the inner geometry and one of the new drawn elements and punch the latter out using Boolean subtraction:

Note that the element which you wish to punch through should have a solid selection, and the element which you are punching with should have a dashed appearance:

resulting in:

repeat until you arrive at:

Note that if you get the selection wrong you can just undo, which will reverse the selection, then redo the Boolean operation.