I know that noise.............
My car one cold day began doing the same thing when first started.
At first it sounded like pilot bearing ( ask me how I knew ) but it occurred very differently from that wonderful experience.
Thought it was the tensioner, but because of the cold I had not selected the AC in awhile. Put it back on AC and after a few more starts..... problem gone.
Has not returned in almost 10 years. So I always leave the AC on.
Why did I say that (10 year thing )out loud!
At any rate, that is what happened to me.
Hope it might help you!
Marty