It is really hard to tell age and mileage from a belt just by looking at it. So, I don't think anyone can tell you this with certainty. Perhaps someone who knows what original OEM belt from 2002 looks like can chime in and say that a version with logos you have was produced from 20xx and that gives you an idea.
My Gates Racing belt that has only 40k on it looks horrible (tiny cracks) and I will be changing it. Your belt certainly does not look 14 years and 146k old, so I'd say it has been changed at some point. But that's a $4000 guess from a guy on the internet.
You can also removed the cover completely, grab an inspection mirror and check the bolts on the water pump, crankshaft pulley etc. for signs that they have been removed/replaced. You would see obvious signs like sockets scratching the area. That should tell you that work has been done.
What I'd do is go to your friendly neighbourhood Audi dealer and ask nicely whether they can search your VIN and tell either printout a copy of the history they have (they will likely not do this due to privacy issues), or write down all the major service performed (too much work for them) or simply tell you whether timing belt service has been done.
Hope this helps a bit.
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