engine noise

loose belt

Could be a pulley itself or the bearing too. Usually Idler pulleys go out first.

the noise sounds more like a bearing for a cam shaft or a time chain and only last for 2 seconds

I experienced this same problem. Found out mine was the idler pulley. Paid about $250 to get it replaced because the repair required lowering or raising the engine to get to the pulley. I was unwilling to lower or raise my engine with my home tools. After this, the squealing at start up was completely gone.