Faulty VW Jetta 1.2TSI timing chain. Driven 30400km.
Car was taken to the dealership after this video was taken, and they changed timing chain + tensioner as well as some other parts (cost 0€ to me, warranty - of course). Problem went away. I drove this car about 26 000km after this, and the sound never came back.
If you have 1.2TSI engine, and think about weird rattling noise when starting your car - IT IS NOT NORMAL! VAG services should be aware of this issue.
