Yeah, this sounds like a case of mixed descriptors, because while a strong odor in the cabin of new Giulias while stopped is typical, the cat pee description is not, but if you think of the common petro-chem descriptors and cat pee as both pungent, noxious, odors, then everything does point to the classic, new Giulia stink phenomenon.
There is no known certain cause or cure for the problem, but as noted above, it does resolve itself in time. I’ve experienced it in both of the new Giulias I’ve owned, and can say that there are a couple of ways to manage it.
First is to get the car hot; put long drives in when you can to heat fluids and components. I’ve got the theory it primarily affects those who purchase in cold seasons, and also those who make, primarily short trips. In both cases, the operating temps are low, so being deliberate to get the car hot seem to expedite resolution.
Second is to turn off both the auto start/stop and auto air recirculation (i.e. turn recirc on manually). The main goal here is to close out-cabin air sources to avoid pulling in the odor, making things more tolerable; ASS activation turns recirc off, which is why you want to hit that button when you start a trip, but also perhaps there is some value to keeping the engine running to help speed that heating/burn off.
Anyway, provided it’s not something else, like the unlikely chance rodents have nested in the car somewhere (which I can tell you from experience is very nasty and durable odor), you should be fine in time. I picked up my current car in early January, had the smell, made some long/hard (1.5 hr) drives, and already at 1600 miles, the smell is gone.