This problem can not be caused by a fuel filter; if it was a filter problem, the car would not run good after restarting. A fuel filter problem does not only occur upon starting.
What is the exact problem: does the car start at a lower rpm as normal? or is it impossible to accelerate normal after starting? or does the car start on one cylinder less?
If the car starts on a lower rpm level as normal, but runs fairly good when accelerating, it is a vacuum problem. The 190D has got an vacuum pod to provide a higher rpm when the engine is cold.
If the car occasionally starts on one cylinder less as normal there is probably one glow-plug going bad.
If the car does not accelerate as normal, but only with half power, the problem can probably be found in the fuel-pump. However, if it is a fuel-pump problem it should occur on a regularly base and not just now and then. The fuel-pump on a 190D is completely mechanical driven and therefore is good or is bad and will not be bad just now and then. The later C-class diesel with the electrical driven fuel-pumps suffer this problem a lot. The C200D is rather good, the C220D needs a new fuel-pump every (approx.) 200.000km and the C250D occasionally has a fuel-pump problem...(but the fuel-pumps on the C220D and C250D are electrical driven).
Personally I think you have to find the solution to this problem in the vacuum system, since it does not occur on a regular base. All the other parts on the engine of the 190D are mechanical and are either good or bad...
with a minor 600+k