The 2.0T FSI is reknown for certain "characteristic" noises, particularly on start-up.
First, the "diesely" sound - this is due to the direct injection. Whilst a good "ear" can notice conventional (manifold sited) fuel injectors pulsing, the direct injection fuel system works at a considerably higher pressure, and so the injectors are slightly more audible.
Secondly, the "tappety" sound actually comes from the camshaft drive chain. If you look at the very useful "self study guide" of the TFSI engine (as found in my even more useful free workshop manuals thread

), you should see exactly where the timing chain is, and then be able to determine if the tappety noise is coming from that area.
However, if any noises appear to be excessive, then a trip to the stealer will be advisable, as will a side-by-side comparison with another GTI.