I built a platform a while back for my gym. Dimensions are the same but I had to cut weird pieces because of the size of the "door" that opens to the room. More like a window, 32" x 32".
I had no such issues with bending. BUT, if its bowed, make sure the bowed pieces are on the bottom. Then they will hopefully eventually flatten. Better yet, don't buy bad wood but too late for that. Its cheap luckily.
Edit: ignore the use of carpet, lol. I didn't have rubber on hand.