Exterior plywood is not a very good back stop for .22 ammo. Even if you put many layers together the sheets will be destroyed in no time by the bullets going through them. I had 1 sheet plywood then 2 layers 3x4 landscape timbers then 1 more sheet of plywood. Seldom did any bullets get through but it wasn't long before the wood was destroyed thus being useless.
Using sand is a very good bullet stop. Think about the sand bags soldiers used during the war and they were used to stop much more powerful rounds than .22lr.
You can take 2x6 boards and make a frame to hold the sand for the backstop. Google it and you will see 2x6 frames with drywall sheeting to hold the sand in was stopping 9, 40, and 45 ammo rounds. That was only six inches thickness of sand. Make two of these frames and put back to back and you should not have any handgun bullets penetrating through. More than likely the no bullets will get through the first frame. I found using truck mud flaps instead of wood or drywall worked much better. The bullets go through the flaps but then the holes close back up some. This worked well for keeping the sand in place in the frame.
I am shooting into 1.5 yards of sand with 4x6 oak planks backstop. I have not had any bullets going through or out of this backstop. I have used 30-30, 22lr, 9mm,40, and 45 with no problems.