Hello,
It will be helpful if you can upload a video during cold start that way, we can hear the noise.
It could be a noisy secondary air pump.
At cold startups the pump does make some noise, however it should not be very obvious. Usually, it is not audible from the inside of the vehicle.
If it is making excess noise the dealership should be able to diagnose and repair if necessary.
I have attached diagrams for your reference.
Please let me know of any questions.
Thank you.
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Monday, January 10th, 2022 AT 9:50 PM