I can definitively say the problem is that the oil used to keep the hydraulic lifters or a timing chain tensioner adjusted is bleeding out when it sits parked for long enough.
Whether that is happening because the lifters or a chain tensioner are worn out or because something like a oil filter drain-back check valve is not working or present in the installed filter, I’m afraid I can only speculate on. One thing really don’t know is what age that starts to happen, or if it happened with brand new cars still on the lot.
I’ve certainly heard the same thing from many modern VW/Audi engines and professionally I consider it normal and harmless, although I find their 4 cylinder engines to be absurdly noisy in general and find that startup noise and general engine noise unacceptable personally. All the ones I see are at least a few years used, near 100k on them, and are still noisy even after the startup rattle goes away. If a car of mine made noise like that, I’d go to almost any length to fix it because it isn’t “right” even though I do honestly believe its not harming anything. It seems like they all do it.
Getting back to the point, I would start by ensuring that a correct oil and filter combination is used. Absolutely synthetic oil, probably 0w40 weight, and a dealer or OEM aftermarket filter from a VW/Audi specialist (would probably also trust a Mobil1 filter). If that’s all in line, I might experiment with using a heavier oil that brings up the low number to a 5w40 or 10w40. I would be thinking about replacing lifters or chain tensioners next, but would certainly spend a lot of effort researching both the lubrication system’s technical data for any design flaws and forum people’s experiences with solving the problem first. If I came up with nothing new in that research, I’d probably shotgun chain tensioners in it and see what happens.
Replacing lifters would involve timing chain removal anyway and it would make sense to do them at the same time as new tensioner(s), but then if it fixed you wouldn’t know which one was bad unless there was something extremely obvious when you examine the parts in your hands. Also keep in mind that I don’t know if your FSI engine is an older style using a timing belt with the hydraulic tensioner in the head for the cam chain, or if it’s the newer style with all chains.