If it's dry now and not smelly, why take it out? just cut a piece of plywood to fit inside the cabinet and let it lie on top of it. You can fasten it in place with construction adhesive around the edges ("Liquid Nails" is a popular brand.) if you like, but gravity and what you place under the sink will probably do a fine job of keeping it there without adhesive.
Best to experiment with some corrugated cardboard and cut and paste a piece which you know will fit through the opening and flop neatly inte place. Then use that to mark the plywood, or cut it yourself or take it to a friend or shop with has the right tools to cut the plywood neatly for you. Many lumber yards or even Home Depot will do that for you.
If you want to get fancy, cover the plywood with "Contact Paper" in the pattern of your choice before you stick it under the sink.
Happy New Year,
Jeff