As Justin and Dan said, you can indeed build the recess from strips. The large, flat forward piece is pretty easy since it doesn't need to bend much. Just build a flat panel and cut it to shape. The back piece needs to bend which may break it.

You can build the flat panel, then glass one side (the bottom) and then cut it out and bend it. The thinner the strips are, the easier it is to bend. 1/8" thick will be easier than 3/16".

I've also cut the parts from birch plywood, cut veneer from cedar clapboards then glassed it on both sides, and laminated veneer onto birch ply.