Plumbing Wall with no studs??

My original tub/shower situation was this: cast iron tub with vinyl shower surround. Two of the three walls are stud walls, the third (where the fixtures were placed) was a 3/4" plywood sheet which formed the side of a built-in cabinet. There is about 16" between the tub and the wall.
The shower valve and tub/shower spout pipes were pretty much pushed through the plywood.
I have removed the built-in cabinet (wood was rotted from leaking) and would like to replace it with a freestanding one, 15". However, the plumbing guy at the store pointed out to me that the shower valve should be secured to a block nailed to studs. Which I don't have, just a cabinet which is 21" deep. I was going to screw a 2x4 to the back wall to have a base to install new tile backer board. So the board would be attached to the cabinet and one stud to form the fixture wall.
My question is:
Can I install some supporting lumber inside the cabinet to attach the block for my shower valve? Is there anyway to make this work and have the valve properly supported without building a new stud wall? I don't mind doing it but the bathroom is so small I would really like to use that space for storage and a pre-made cabinet is going to be more practical.
Thanks!!

That is the way it is done. Starting the screws at an angle halfway in the blocking makes it easier but nails are advised for being a sturdier install.

blocking

The valve has to be secured to "something" not necessarily a 2x4. It is possible that the cabinet itself is all you need, but we cannot tell from your description because we do not know the spacing you are working with or how it will be arranged.