Update: Now that I see your opening size, and the way the counter top creates the bottom sill, I favor Huesmann's answer. It's simpler in this situation and will look nicer.
An alternative to relying on friction fit would be to use double-sided removable foam tape and set upper and lower plates of 2x2 or 2x3, then fit studs snugly at each end and the center to add some compression. These wouldn't even need to be fastened--it won't move once the panels are installed. Fill with 1½" or 2" foam panel and cover it as described in that answer.
Before you begin installing parts, set your panel material in place and trace the opening. Cut ~1/8" smaller than that for easier fitment (assuming you plan to wrap the opening with molding). Cut from the back side to reduce tearout.
Sandwich it.
Since the opening is so wide, I suggest laying a faux bottom plate across the counter top to support the panels. Cut a piece of board to a comfortable length and use two strips of removable double-sided foam tape to secure it. This board should be the same width as the dimension from outer face to outer face of casing (or use two boards, each flush with a casing face and with cross-blocking screwed to the tops to keep them parallel).
Cut two facing panels of your choice of plywood, fiberboard, or whatever. These should be oversized to cover the casing in a way that looks decent, and they should be fairly rigid (self-supporting*). Maybe just larger than the outer casing dimensions would create a clean look.
To one panel, attach one or more foam panels that just fit inside the actual opening, to deaden sound. Use panel adhesive, double-sided tape, etc.
Ring the casing with removeable double-sided foam tape.
Press the panels in place. Depending on what panel material you chose, this may be all that's needed. If it feels solid (check after a couple days), all good.
If not, drill through both panels just inside the original opening at a few points and squeeze the assembly with long bolts and barrel nuts ("sex bolts") or similar. With just a bit of tension there should be plenty of friction to keep things in place, especially if you fitted the foam bits well to the opening.
Now, if you want to restore the original cased appearance, install new casing over your panels. This could also be mounted with panel adhesive or foam tape.
If you want to get really fancy-pants, fit 1/4" plywood inside the existing casing, just lapping onto the frame (about 1/4"). This takes a lot of precision, of course, but might give the cleanest look. See my note below about thin panels.
* If you want to use thinner panel material, bond rigid 2" foam to both panels to add stiffness, fitting inside the original opening.