I have the same problem with my 1967 Mustang 200cui C4.
It is not the belt!
The sound comes from the starter or anything near the starter.
It gets worse once you hit the gas.

Has anyone a clue?

 

Too vague. Too bad you can't post a sound. If the starter bendix hangs up, it can make a Gawdawful sound. Very quickly destroys itself and the flywheel gear, though. This is particularly expensive on 6 cylinder auto trans cars.

 

The power steering pump itself may be noisy. Another possibility is the alternator. They aren't warmed up and may be complaining.

 

I think that it is the muffler bearing. You need to add a pint of blinker fluid and it will cure the problem. You can find this at Autozone. I bought some last time i went snipe hunting.