Lap the carpet over the edge and staple is mentioned, I would get some double face carpet tape and place two or three strips along the length, dividing it equally from the sides. I'd staple one side and lay the tape on the plywood, then pull to the other side patting it down as you pull it across. Over some time the carpet will stretch some and that should keep the carpet from bunching up and getting wrinkles. It also depends on how heavy your carpet is, the heavier, the better it will lay and the harder it will be to lap over and staple. You could also use "Z" bar along the edges on the sides to hold the carpet. That Z bar is used at door thresholds to make a transition from carpet to another flooring.
Carpet glue is not that hard to rip up old carpet and smooth out for another carpet and would be better. Depends how long you want it to last and stay down. The carlet will last longer the less it can move.