A precast concrete slab will work just fine.
The key is to use a double topping slab.
The configuration would include(bottom to top):
precast slab +
concrete topping for leveling+
weatherproof/waterproof membrane+
concrete wearing surface
Provide a nominal pitch to keep the water out as best you can.
You can get flat precast slabs to go the spans you require, and for loads more than what you would probably require.
It will not be cheap, but it will be a very good system that will install very fast.
Regards,
Yooper Dave