2001 Acura Integra LS Automatic transmission with 128k miles. This noise happens intermittently, it's coming from the engine bay, and it happens more when it's cold out. In the video, when I start the engine in park it's silent. Once I put it into Drive it starts, about 3 seconds in. When I put it back into park it stops. Of the times it's making the noise on start, it goes away/becomes more rare once I start moving. A similar noise also shows up sometimes when I'm driving, usually at high rpms or when I'm pressing on the gas just a little bit. I would describe it as a grinding/rattling.
I took it to a mechanic and they said they couldn't reproduce the noise and didn't notice anything wrong with the engine bay besides a small oil leak in the head gasket.