We had an almost identical situation in a former garage that we refinished to be an office. Our contractor suggested this and we liked the result: he installed a piece of wood about an inch out from the concrete, putting insulation between them and keeping the wood a consistent and level height - a little higher than the concrete. I can't remember if it was pink fluffy insulation or spray stuff. Then a shelf about 6 inches out from the wall - nice and level by being a bit up from the concrete and supported by the vertical wood, and there's insulation under the shelf too. The whole thing is a good looking clear pine and is well varnished.
![low shelf](https://i.stack.imgur.com/X25jc.jpg)
Looking from the side gives an idea of the distance from the wall:
![side view](https://i.stack.imgur.com/vJpaE.jpg)
The shelf runs around the entire room and is remarkably useful for something so low. It hides all the lumpy bumpy aspects of the concrete and while it's not something you see everywhere, no-one has ever mentioned it so it can't be that unusual.
Rooms above garages are often done improperly. It's amazing, because it really isn't all that difficult, but a lot of people seem to mess it up.
Unfortunately, there's no "easy" way: You're going to have to remove some drywall to inspect and see how the insulation in the ceiling is done. There may or may not be a gap in the space, depending on how the ceiling was done. Even just taking the temperature above the insulation in that space will tell you a lot (above the insulation, it should be close to room temperature).
Drafts in that space are absolutely killer, it means there is a direct source of outside air. Black on the insulation is a good sign of airflow, indicating drafts.
![enter image description here](https://i.stack.imgur.com/06sr3.jpg)
Basically, if the ceiling space isn't totally sealed, the only thing you can do is turn the garage into a conditioned space (very expensive, in terms of both construction costs and ongoing energy costs), and even then, if the problem is between the insulation and sub-floor, it won't help.
What should be there at a minimum is a continuous vapour barrier, with a layer of insulation on top. The vapour barrier should be sealed to the subfloor or the vapour barrier from the walls above. The insulation should go all the way around the edge (in the headers), so the insulation is continuous from the floors up to the subfloor. There should absolutely be no drafts, exposed concrete, or anything directly connected to the outside that is uninsulated.
![enter image description here](https://i.stack.imgur.com/YDiMK.jpg)
The best way (in my opinion) to seal this space is to use closed-cell spray foam, and form a continuous seal across the bottom of the entire subfloor. This gives you great insulation, no drafts, and acts as a vapour barrier as well (vapour barrier is not needed in this case -- though some building inspectors still don't understand this, so check your local codes). It also is better at ensuring fumes from vehicles in the garage can't get into your living space (in theory, vapour barrier prevents this as well, but 6mil vapour barrier is easier to puncture than a couple inches of hardened foam).
![enter image description here](https://i.stack.imgur.com/pgLYK.jpg)
Though you may be able to find something obvious and fix it, be prepared that there's a possibility that the only "fix" is going to be to completely tear down the ceiling of the garage and re-do it properly.
If you're going to spend money and time on this, do it right.
Best Answer
Are the walls insulated? If not, do that first. Most of the heat escapes there...especially the part nearest and above the ground level.
With a fully insulated wall, you might not even need to insulate the slab. in MN we insulated our walls and then left the concrete floor as-is (stained it). Only on the coldest winter days did we need to turn on the fireplace and when we did, the slab was fine comfort-wise.
Otherwise, the most typical way to insulate the slab will be with foam board. Typically EPS or XPS with a floated plywood subfloor on top.
But if you have no intention of ever finishing the basement, maybe insulating the first floor underside might make more sense.
UPDATE
The above is valid for a house with a basement. I misread your question initially. It appears you have a floating concrete slab as your foundation. To insulate that you need insulation...either under it (preferred) or on top of it. Obviously adding insulation underneath is not practical after the fact.
The cheapest solution is likely just a new floor covering...carpet with a think pad...maybe cork, etc.
More complicated, but doable, would be to lay down EPS or XPS and then a floor on top of that. The trick there is that this will change the height of your floor...likely causing issues with doors, thresholds, cabinets, etc.