Weak start on the S 320 cdi W220?

Hello everyone, first of all I would like to introduce myself. I am Matthias and am already proud owner of an S220 built in 1965. Now I would like to buy and drive an S-Class as a everyday vehicle. Specifically it is to become an S 320 cdi of the series W220. After I have read in the forum diligently and at least got a rough idea about the weaknesses, I was allowed on Saturday, at a larger car dealership nearby, for the first time in a S 320 c I was surprised and disappointed by an extreme starting weakness. Even with a warm engine, almost nothing happened when starting from the stand. Only from about 2200 rpm it felt as if a switch was being changed and there was suddenly power. It really felt as if the vehicle had no power at all. Under 2000 rpm there was no trace of torque, so even an E 240 T w210 looks like a racing machine… Well, my question: has the “old” in front of Mopf engine with 197 hp such a crazy turbo hole? Thank you in advance. Greetings, Matthias