I'd suggest getting a stethoscope and checking your idler pulleys. What happens if you have the AC on during start up? Same noise or different?
I'd also use the stethoscope on the accessories and waterpump. Maybe move the exhaust heat shields just a bit to see if something changes.

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2001 x5 3.0 (sold with broken motor), 1990 e30 M3, 1991 318is, 2002 325i, 2008 335i Dinan stage 3 6 speed,