One of the best part of taking home a new vehicle is the new car smell.
Burning smell? Never in the decades of riding and owning a newly purchased vehicle has it ever had a burning smell?
Did you test drive it or just wanted a certain color and bought it on the spot.
Bad craftsmanship or perhaps oil or liquid was spilled in the engine. Anyways, that smell would annoy or give some passengers a headache.
Perhaps the dealership could give a carbon cabin filter, use some air fresheners for now until it goes away.
Seriously the only time I had a burning smell in the 14 yrs I owned my rogue was after my radiator leaked out all the coolant and I smelled something burning and then eventually saw steam rising from my hood.