The way I built my barn for my goats might help, but you may have to temporarily lift the shed.....not sure if the size is manageable.
Under the bottom plate build up a stone or even block foundation with the joints un mortared, and even run some perforated drain pipe if in a really wet area. This will need to be a total hieght addition of a foot or so.
Start with a base of 3-4 inch limestone riprap and tamp it in really well, then some landscape fabric on top, maybe two layers. Then fill the next layer with no2-B limestone and pack that down really well.
On top of this I did
pea gravel, but the cows hooves are a lot tougher than goats, so you might do better with a layer of 1/8 to dust limestone that will pack down and create a floor that will take the weight.
Then I still bed them in with straw, the whole thing drains and the rainwater passes undernieth naturally without issue.
Like I said, might not work if you can't lift the structure, but if you can, or if you are building I highly recommend it.