Ellie,

There is a type of cat litter called "Yesterdays News". It is a pellet type of litter that is made out of recycled newspaper. It is soft on their feet, but it absorbs very well.

Because the pellets are large (it's not like regular litter which looks like sand) you could just pour a pile of the litter pellets right on the floor, and then vacuum them up if they are unused, and use papertowels to grab them if they are used/wet.

When we got a cat over the summer, he was 9 months old but because he had previously lived with a lazy guy the cat had a habit of peeing in the bathtub.... I used the "Yesterdays News" type of litter by puring it on the bottom of the tub... that got the cat accustomed to peeing on this litter so it made it easier for him to adjust to using a litter box properly.

And because the pellets were large it was easy to keep them from falling into the drain, and it was very easy to clean up the used and unused litter.

So, maybe using a pile of these yesterdays news litter pellets on your floow would help - and then once your dog is accustomed to using the pile on the floor, maybe you could easily train the dog to use an actual litter box.