If your ground gets wet from underneath, you need a floor in the ark.
If it's light well-draining soil, with a water table always well below the surface even in the wettest of winters, then you might get away with it.
Another way I've seen it done is to have the ark under cover - in woodland (but think about how bare its 'roof' will be in winter), or a tarpaulin piggy gazebo - so the rain doesn't fall on or around the ark. (We can't do that here - too windy.)
I do have a weaner house in a raised sheltered spot in an orchard and protected on two sides by high walls where I can get away with no wooden floor - but there's a layer of old tyres under the thick straw bedding, just in case.