This is just a guess based on my experience. Low residual fuel pressure.
I'm going to use a water hose as an analogy.
When you turn your car off fuel should be trapped in the line under pressure. The injectors act as a nozzle. The fuel lines as a hose. And the pump as the valve. If you turn the valve off and the nozzle is closed the hose will still have pressure. This pressure is what give you immediate starting. If the valve (fuel pump) is allowing pressure to bleed off into the tank then it will take 5-15 seconds for the pump to push fuel from the tank to the injectors and the car will sputter and mis until the pump has pushed fuel pressure to spec. Take it back and complain of the exact same thing this time leave it overnight. If they don't see the problem contact soa.
I have seen this problem on other vehicles in my profession. Though rare it mostly happens within the first 2-3 years.
Good luck. Understand that this is an educated guess. Since I can't put my hands on your car this is the best I can do.