Making a “ledge” to hold the glass will work, of course, but you’re left with a visible bump just under the glazing which will need to be finished like the interior of the rebate. Plus, should you ever have to disassemble the frame, the job will be a pain.
I prefer to use a “box” made from mat (mount) board and strengthened by foam board. We use suede a lot, since it seems to go with the things we often mount like military medals and wedding accessories.
Determine how deep your shadowbox needs to be, say, 10 cm, and the horizontal and vertical dimensions of the “background”, say 80 cm x 20 cm. Add 20 cm (2 x 10 cm) to each dimension, so that your starting mat blank will be 100 cm by 40 cm.
Reduce the depth of your mat cutter blade (the bevel side) so that the blade cuts through the backing
almost,
but not quite, slicing through the surface paper. You will probably want to play with mat scraps to get this just right.
Set the guide bar to 10 cm and score the back of the mount board on each of the four sides.
Remove the four corner pieces, but leave the exposed surface paper. If you’ve scored the back just so, the pieces should be easily removed without any mat board (mountboard) “core” remaining.
Gently fold each of the four sides up at a 90° angle so that you have the makings of a box. Fold the exposed surface paper into a triangle, then tape each triangle flush against the exterior sides of the box. I use “licky-sticky” linen tape; it seems to hold better. The triangles also should be taped in opposing directions so the “box” doesn’t get skewed once you frame it.
Once you’ve got a semi-rigid box, cut strips of foam board the full length of each side plus 5 mm (the thickness of the foam board) by the height of the sides of the box. This height may be just a wee bit more or less than the 10 cm you originally scored. It depends a lot on just how deep the blade was set and the actual thickness of the mat board, so you should probably measure it rather than rely on your guide bar.
Adhere these foam board strips to the exterior sides of the mount board box. I tend to use PMA since I don’t need to apply a lot of pressure (and risk distorting the sides of the box) to make the bond.
You are left with a “seamless” box that transitions from the back to the sides with no sharp, glaring gap between the two surfaces. And, I believe that one has a more pleasant color (usually) seen at the side of this shadowbox than a stark white or black hunk of foam board.
Place you glass on top of the box; the rigidity of the foam board should keep it from collapsing. Fit your frame over the mout/glass package, and voilà.
Another advantage to my mind is that this reinforced “box” is self contained, so it shouldn’t need to be afixed to the rebate. It’s a lot easier to remove from the frame if the need arises.