2004 pt cruiser timing belt and water pump?

Squealing on startup is almost always the alternator belt. The alternator load is heaviest when it is trying to recharge the battery from starting and the belt is slickest when cold. The mechanic is shining you on about it being better after it wears.

It may be quieter but that is only because it is slick where it has worn and is working worse. You should find somebody more interested in doing it right to replace the belt and properly tension it.

Check all the bearings maybe its the crankshaft it happened to me it was 24/7. And my ac compressor bearing bad so it only squeals when I rev it from .5k-2k.