It's likely to be drywall, or plaster depending upon your location. I've never seen cabinetry installed against studs and then drywall installed after.

Can you not open doors below cooktop and see wall behind cabinet? I've replaced cooktops with free standing ranges without replacing cabinet or countertop if that interests you. .

Could be any of the above. In 1963 I'd guess plaster or similar, though that's also around the time drywall became commonplace so could be that too. Our house is older (kitchen was last renovated before our remodel in 1939) and had some on plaster and some right to the studs. Also, some on the subfloor and some open to the crawl space below...!!!

(And yes to just opening it up to take a look.)

I have a house built in the '50s and you can't look thru a cabinet to see the wall--the site built cabs have solid plywood backs. (Most garages in the development now have them in the garage. They are unbustable.)

You would need to drill through the back to open it up and see what’s behind. You should be able to tell quickly if it’s wall or bare studs.

Thanks everyone! I'll try see behind it.

You might also try looking behind your fridge. In a 1963 kitchen, I would expect the cabinets to stop at the fridge (no fridge surround), but drywall behind the fridge. So you could look at the starting edge of the cabinetry, and whether the drywall seems to run behind the cabinet, or butt up against the cabinet side. To be extra-sure, measure the distance from the front of the cabinet to the back, on the exterior and interior.

@mcarroll16 you'd be surprised--our 1939 kitchen had a fridge surround! (Sadly too short to accommodate a modern refrigerator--that was in part why we remodeled years ago--but ahead of its time nonetheless.) It did have plaster behind the cabinet box, though.