I'd cut a piece of plywood that is about 3" larger than your existing hole. Drill a pilot hole in the middle of it. Get a stick of wood that is longer than the hole by maybe 6"...drill a through hole in the middle of it. Put a bead of silicon around the whole piece of ply, get it into the hole in the shower...orient it so that you have as even an overlap you can around the existing hole, pull it towards the back of the wall while tightening up the screw to then act as a clamp to pull it up against the back of the shower wall. Leave it overnight for the silicon to cure (or, you could use epoxy resin, and not need to wait as long). Once it is secured as a backing board, remove the screw and the clamping board from the front surface.
Get some car repair fiberglass sheets along with some epoxy resin and hardener...mix up the epoxy, and fill in the hole, extending the top layer of fabric (you'll need more than one layer to build up the depth you need) to overlap the existing hole's edges. Let it cure, sand flush, paint if you want to make it look decent, or just leave it until you can replace the whole thing. You can do this for not much money, and you don't need to worry about how it looks.
If you want it to look good, you can pay someone, but if you are careful, and then can get a suitable finish (like what a pro would use), you could make it look as good as new.
You could also get something like a piece of plexiglass, epoxy it in place from the front that would work as a temporary repair.