It would have to be something that runs off the serpentine belt - either the power steering pump, alternator or the waterpump.....the alternator can screech on starting if the belt is old and dry and stretched, although it's not really common with serpentine belts. Same with the PS pump but that's usually when the steering is on full lock. The water pump would screech if the bearings were shot, but it would do it all the time.
It could be the tensioner not giving enough tension as well.
If it was me, I'd remove the belt, inspect it to see if it's shiny on the ribs or if any ribs are missing...if they are I'd buy a new belt. If the belt looks OK then try spinning by hand all the items that run off the belt - look for stiffnes/roughness.....do this before you start the car when it would normally screetch. Also look closely at each pully for black skid marks left by the belt when it slipped. If nothing turns up from this, try some 'belt grip' on the belt just to prove that it is the belt (you can buy this product but I'd google for a more common substance you can apply and costs nothing).
Good Luck.
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