My 2003 Aviator makes a harmonic rattle on cold starts that disappears if revs are above 3k rpm or 5 minutes into warming up.
I've replaced the 3 drive belt pulleys and pulley tensioner.
Also replaced the fan clutch.
A/C engaged or disengaged makes no difference in noise, neither does turning the steering wheel to activate the ps pump while parked.

I've searched a lot, but only thing i can guess is timing chain tensioners?
Truck has 138k miles with unknown service history.
Can hear the noise here: seems to come from front of engine near middle.
https://www.youtube.com/watch?v=BKH5...ature=youtu.be

 

It's a bit difficult to a good sense for the noise over cellphone and PC fidelity. Are you quite confident it is not an exhaust manifold leak? It's pretty common for exhaust manifold studs to snap on these, particularly on the passenger side. From over the passenger side upper control arm and with a good light you should be able to get a good view of the manifold studs. See if any are missing or broken.

-Rod