I am assuming that you have limited woodworking skills and or tools? Is that correct? Following with that I am guessing that routering out the frame isn't likely. If this isn't accurate just ignore this routering is neater do it that way.
You can use a split system, If you use plate glass that is 1/4 inch thick and you figure the frame should be 1/2 to 3/4 thick or so you could use lets say a cut out 1/2 plywood door with the hole for glass then cut 1/4 spacers to go partially around the door but not as wide as the frame, then a second piece of ply the same size as as the first and basically build a sandwich. Plywood top side a 1/4 spacer frame with the glass window (if you do this leave a small gap around the glass 1/16 or so wood will alter shape more than glass so you have a bit of space for this) and then a back piece and you can then screw then together (if you glue it and the glass breaks you have a big job ahead of you.) If you get the lumber yard to cut the sheets for you all you need is a screwdriver and maybe a drill.
Alex