Condensation / damp from garage floor. Can it be fixed?

I've got a basic garage in the backyard - essentially a sheet metal shed with a concrete floor. It would have been built in the 1980s so I doubt the concrete slab had a water barrier - or if it did it probably wore away over time.

When we have wet weather, the concrete gets damp underneath items on the floor - like rubber mats etc. There's also some mineral staining. Doing some reading online, it looks like concrete efflorescence.

I'm considering demolishing the shed and building a better workshop (insulated etc.) on the existing concrete slab. Can I make the existing slab a usable floor by sealing it with something like epoxy? Or would I be better off using the slab as a footing and building the new structure on posts with a separate floor suspended above the slab?

My goal is to avoid getting any damp or mould in the new structure.