Looking at the picture, a regular piece of wood should work as long as the thickness is the same. Otherwise the front will sit a bit proud if thicker, or there will be a gap if thinner. Though you could trim the dado back on the sides if it’s thicker.

It looks like that particle board is nailed to the face. Hopefully it isn’t glued as well, otherwise it’ll be a beast to get off. Those screws are just for the handle and likely have no structural qualities.