My 06 Azera is making a clicking noise during acceleration on cold starts. It sounds like a valve noise like a lifter not getting enough oil. The oil level is fine been using 5w30 since I bought the car. The dealer said they couldn't duplicate the noise so they dismissed it.
clicking noise on cold start-up on 2006 Hyundai Azera
First thing that pops out at me: Your car takes 5W20, not 5W30. This can cause some engine issues, so please make sure to use the correct grade. That could be the entire answer to your issues.
I had the same problem took it o dealer and they fixed the problem, bad lifters