Might be your main flywheel. I had a squeal in a car I owned once. I hosed down the hub where the shaft mets the wheel (staring you in the face when you open the hood) with WD40 and it took car of the problem for a while, then I have to hose it down again.
If you do it make sure you don’t spray the inside of the wheel/pulley area.
There’s lots of routine maintenance you can do on your own car once you have someone show you what stuff is and what it does under the hood.
If it was the flywheel, wouldn’t it squeak continually, though, and not just when idling+cold?
I know I should probably know more than I do...but at the same time, I know how lousy I am with hardware in general, so I hesitate to really delve into it. I might be able to speak with more authority, but I still don’t think I’d want to do the actual work. Not on something that’s liable to kill me if I get something wrong...