The way forward is to find out what happens in the first few seconds when the engine is started. The fact that there is no noise for the first one or two seconds almost certainly discounts a lack oil pressure as the cause.
I think that the start procedure is very similar to the one used by the E46 M3. The VANOS is in the default position for start up, the engine cranks and fires and after two or three seconds the ECU take over control of the VANOS and makes an adjustment. At that instant a noise is produced in some cars by that action of the ECU - understanding what that action is should point to a fix.
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