UPDATE:
We tried to duplicate the noise but it wasn't possible because the car doesn't do it when it's warm. They took the belt off and inspected everything and saw two things that
MIGHT be the problem...
1.) Number 6 pulley was slightly wobbly - it had a little play (idler pulley).
2.) Number 9 pulley was slightly difficult to turn (tensioner pulley). I mean it turned, but not as freely as the other ones.
Since Ford parts was closed in that area, we couldn't do anything about the tensioner pulley because I just needed the pulley itself. The shop that was available to them only sold the package (tensioner arm and all). At Ford, you can supposedly get the pulley alone.
The other pulley (number 6) was available from their parts provider and it was made aftermarket by Gates. The quality was very good - even better than Ford's crap.
So, he changed the idler pulley and rechecked everything. He put the belt on and started the car and low and behold...the stupid *&$#@#$ noise was there. It was very faint though and didn't last long because the car wasn't really cold. It needs to sit over night OR a few days for it to be very noticeable.
So now, the problem is either the tensioner pulley that is slightly difficult to turn or it's something else that they can't determine without hearing it right there on the spot.
This situation is very weird and annoying.
Again, all suggestions are welcome. The shop wants me to leave the car there over night so they can start it and hear the noise in person in order to determine what it is.