Had that issue with my 2006 Audi A3. Expensive fix as it happened a year before the tsb or recall was issued. Got the voucher after I got rid of the car, no compensation if I didn't still own the car.Sounds an awful lot like the HPFP (high pressure fuel pump) or an injector having issues. The MK V GTI's with the BPY engine had issues with a component called the Cam Follower. It was a cap that fit over the HPFP plunger that ran against the cam lobe. The cam followers were failing, and wore a hole in them causing the HPFP plunger to grind against the cam lobe. Some of them made a similar sound as this.
The injectors are also known to make noise but this is not a sound typical of those. If it does this only when the engine is cold it could be something in the EGR system. If it's doing this all the time and the dealer you took it to cannot even inspect it for three weeks (unacceptable in my opinion), then definitely take it to another dealer since this noise is clearly something mechanical in nature and could present a serious engine problem.
Yeah my '08 GTI was at the dealer for three months because of the HPFP and camshaft shortage. Mine punched through the follower and had nearly ground the retention clip off the end of the plunger before it started acting up. At least they put me in a loaner while they had it. They replaced the pump, cam, follower, dropped the pan and replaced the oil pickup tube and cleaned out the pan. It went in with 26K miles on it and I put another 120K hard miles on that engine. I made it a point to check the follower at every oil change. Had to replace it three times because even the upgraded part would start showing wear after about 15K miles.Had that issue with my 2006 Audi A3. Expensive fix as it happened a year before the tsb or recall was issued. Got the voucher after I got rid of the car, no compensation if I didn't still own the car.
I would think some fueling issues would surface that would be noticeable while driving. That noise is concerning.
My A3 became cursed. Started with rodent chewing wiring harness, dashboard flashed every light and warning possible, ECU toasted. Got that fixed, week later battery died, got that replaced. Car ran great, month later HPFP follower decided to chew itself up. They had the car for a week, replaced failed components. Drove great for about a day and then fuel injector problems. Traded it on a 2010 A4 before the A3 was worth less than cost to repair. The A3 went to auction. What sucks is I really liked that car. The 2.0 turbo and DSG trans was a nice match.Yeah my '08 GTI was at the dealer for three months because of the HPFP and camshaft shortage. Mine punched through the follower and had nearly ground the retention clip off the end of the plunger before it started acting up. At least they put me in a loaner while they had it. They replaced the pump, cam, follower, dropped the pan and replaced the oil pickup tube and cleaned out the pan. It went in with 26K miles on it and I put another 120K hard miles on that engine. I made it a point to check the follower at every oil change. Had to replace it three times because even the upgraded part would start showing wear after about 15K miles.