You could cut the Sheetrock out to the studs. Add a board at the bottom. Finish the back side of the Sheetrock and the wood. I put contact paper on mine.

Cathy: maybe this will help

https://www.familyhandyman.com/woodworking/shelves/built-in-shelves/

Here is my favorite one.... https://www.youtube.com/watch?v=PsrjXGGSqGM&t=257s

https://www.hometalk.com/34683331/q-how-do-i-make-a-storage-unit-with-shelves-between-wall-studs

https://home.howstuffworks.com/home-improvement/household-hints-tips/cleaning-organizing/how-to-maximize-storage-space5.htm

https://www.remodelaholic.com/brilliant-in-wall-storage-ideas/

What type of items are you planning to store in your new found space?

Here are some other examples of how this floor-saving storage can be used:

Is the wall sheetrocked or open?

This is a pantry, but you could use it for inspiration. https://www.hometalk.com/18155865/pantry-between-the-studs

Pantry Between the Studs

You need to add wood for shelf’s then cover wood with sheet rock and paint

Cut and demo the drywall so that you can expose both side of the studs.

Cut the 2x4 shelves to fit and have someone hold them in place, while you glue and screw them in from the other side of the stud. (2x) This “blind screwing method” should be fine as long as you don’t store three stacks high of heavy canned goods, side to side.