How to make this face rounded?

hi, i’m working on a project and i can’t quiet wrap my head around making the back of the object round to where it looks puffy/stuffed while keeping the original shape. is there anyway I can do this?

Not sure entirely what you mean by puffy/stuffed, but I can see straight away that you have a non-planar face made of an n-gon. This can be a problem with getting any shape as faces are supposed to only be flat. Stretching the vertices so they aren’t flat can make some unexpected shapes. You would want to subdivide the face into smaller faces instead to keep the curving shape.

By pufffy/round you mean you want that face selected to curve into a convex shape as if it were a fabric with stuffing filled in behind it, this would also need more geometry to do so.

There would be lots of ways to do this. You could sculpt it, do a fabric sim, edit faces manually (but with proportional edit to get a smoother look), bevel the edges, etc. I would say to just use propertional edit first as it is a pretty easy method that would help in figuring out how you want it to look.

If this look works for you, then a very simple workflow is:
Inset the big Ngon face by a certain value (the higher you set it, the smoother it’ll be, but the more cleanup you must do).

Some verteses will intersect each other, clean these up manually

Add some supporting looks around the parameter, and apply a subdivision surface modifier.

If you dont want the high poly look, then duplicate it, follow the steps above, then model the low poly version on top of the high poly with a shrink wrap.

To keep sharp edges, use the Crease Edge function.