Your concerns are justified. It is called hydrostatic pressure. You dont describe your home, but I envision a raised ranch type home with the garage on one side on the lower level with living space above. Most of these homes are build on a concrete slab and typically they are about two to three feet below grade.
Your safe, you dont say what kind nor do you say if it is flat on the bottom or has some sort of feet or platform underneath, pushes down on the concrete which in turn is pushing up on the safe. If it weighs a few hundred pounds, probably not a problem. If it is a large heavy duty model, it may weigh many hundreds of pounds which might be a problem.
For example I lived in a raised ranch in Connecticut. The water table was only about 25 feet below my home. When I left my car parked in the garage for a few days and then moved it, there were damp spots on the concrete where my tires rested. Not water, just damp moisture spots.
So yes, I would recommend setting it on something flat to distribute the weight evenly. Something like a 3/8 inch sheet of stainless steel or a sheet of resin cut to fit the bottom of the safe so you dont see it. When you move, dont be surprised if you see moisture effects on the laminate wood floor underneath. Someone said to buy an extra box of the flooring, good idea. I would not bank on your vapor barrier, a sheet of felt tar will only do so much.