Our 2005 'B' does the same and has done for many 1000's of miles.
In our case it is the hydraulic tappets and not the variator. Basically the tappets are draining down oil overnight / during day or a long duration stop.
Like the variator noise is does no harm but is very annoying till you accept that it is normal behaviour.
Problem improves alot for the first 1000 or 2000 miles after an oil change.
If it was the variator then the noise would be there all the time. Also when the variator does start to wear then you will start to notice the diesel sound driving normally but ONLY in lift off conditions. Rest of the time there will be no noise. As the wear increases then the rattling will start to happen all the time.
Not sure what engine build tolerances / changes were made on the later 1.8ie Punto HGT/Barchetta/other engines but I gather cold start hydraulic tappet noise is far more common on the later engines and at lower mileages. Often sounds like a bag of nuts loose in the cylinders.
BS, my variator is making horrible noise after WARM start up for a few seconds. has to be due to wear. (has been changed 2 years ago)
But; it can be the starter. That has been for 2,5 years a verry annoying sounds on almost every start up. More like a grinding noise.
Both sounds don't really harm but verry annoying.
Problem 1 caused by too low viscosity oil( 5w40) but it has other advantages.
Premlem 2, too much of a hassle to fix
tappets have been noisy with me too. an oil change will fix that. 10.000km are max. 12.000 and they are noisy with me
OR...they are worn and need replacing (could also be worn camshaft)
