The timing belt isn't the likely cause of the noise. However, the serpentine belt is.
Based on your description, it sounds like there is a problem with the idle air control valve (IAC). The IAC is responsible for maintaining engine idle speed. Here is what I suggest: The first thing I would do is check for engine vacuum leaks. Here is a link that explains how that is done:
If none are found, next is to remove the IAC, inspect it for carbon build-up/dirt, and clean it and the airway it plugs into. The IAC is located on the throttle body. I will need to know the specific engine you have and if it is turbocharged to get specific information, so let me know.
We do have a procedure for servicing the IAC, but based on the engine, it may be recommended to avoid cleaning.
Let me know if you find leaks and the engine size.
Thursday, November 4th, 2021 AT 8:43 PM