If I had to guess this sounds like a four cylinder engine, with one or even two cylinder's misfiring. Best guess is a problem with either a spark plug wires, or an ignition module. I'm looking at high resolution photos of your engine compartment and its not clear on what type of ignition system you have. Generally there are two types of systems. One has a single ignition module, and then large diameter wires that lead to each individual spark plug. Another design has small wires leading to small seperate ignition modules placed right over the spark plug. My guess is you have the single ignition module with seperate wires, and one of those wires has an intermittent short to the the engine block. When that shorts out, one cylinder isn't running correctly, and the engine will be very rough. Unfortunately all of your ignition wiring is hidden on the back side of the engine, under the black plastic cover (between the engine and the dash panel sheet metal.)
Do note, this issue could be something as easy as a spark plug wire not securely attached to a spark plug.
One easy test (if you can see all the wires) is to run the car in a dark parking lot at night (obviously in neutral, with parking brake securely fastened.) With hood open just look for evidence of little blue sparks anywhere around those wires. NOTE: Do not put your hands or any part of your body in the dark engine compartment. There are a lot of moving parts and that's just dangerous. (I caught my hand in an alternator fan at night Thwack, and it still hurts to think about it.) Please be safe!
One thing about ignition faults.. they don't always set a code. I've seen codes set in cars with coil on plug systems, but I've also seen vehicles with single ignition module, with visible shorts to the spark plug wiring that do not set a fault code at all.
Note: there is one other thing that can cause rough engine idle. If there is an Exhaust Gas Recirculation (EGR) or Vacuum controlled device that gets stuck open that could adversely affect engine idle. Generally those defects will set an fault code.
Were I in your shoes, I'd start with a test of all the engine fault codes. Then I'd inspect the ignition wiring for signs of decay (or shorting out.) Often you can see carbon marks where the wires short out on metal parts. (That inspection is done engine OFF- Safety first!) Let us know what you find.
One comment: With a car that new, isn't your manufacturer's warranty still in effect? With your description, this issue should definitely be covered under warranty.
Edit: You've mentioned this issue is only observed when the car is first started in the morning. If it was forty years ago, I'd be looking hard at the automatic choke on the carburetor but not with a new car like yours. You've got fuel injection and control mechanisms to monitor engine temperature and adjust air fuel mixture. It's possible a temp sensor is bad, but that will definitely set a code. I doubt it, but it's possible. Again, first step here is to read the stored fault codes.