Following everyone's suggestion, I used 1/2 inch hardware cloth to fence in the floor of the hutch to the bottom of legs, which is 1 inch away from the cage floor.
The front panel is 2x2 inch welded wire, and I covered it with 1/2 inch hardware cloth as well. I had to make a square cut on the hardware cloth to leave the cage door accessible, cover the door itself with hardware cloth too, and then had to do some metal wire stitching job to fix the cut around the cage door, then apply tapes so no protruding wires to hurt anyone.
Looks quite ugly but at least more convenient this way compare to if I use a whole piece to seal the door inside (there is a wooden door on the nest box but can not access the wired area through it).
The two sides of the hutch are 1/4 inch thick lumber, and I enforced them with another layer of plywood board, to make it about 1/2 inch thick. Is that going to be enough?
The back of the hutch is a plywood board of between 1/4 to 1/2 inch thick, do you guys think I should enforce it with another layer of plywood board, or for peace of mind, just cover it with 1/2 inch hardware cloth too?
Also the roof of the hutch can be opened on two hinges, the roof itself is fairly heavy because it is covered with a layer of weather resistant material. Would it work if I just put some heavy flower pot on top of roof hoping coon can not open it, or should I lock it down instead?