I asked my German mechanic about my dad's car while looking into a hard start condition. I asked if it might be a fuel pressure regulator and he said no. My dad's car, 1987 300E, rarely starts on first attempt. Always starts the second try though.
The mechanic said that when the fuel pressure regulator is bad the car runs rich, which makes it smell like rotten eggs. I belive he also said that it happens when cold or just started. I would HIGHLY suspect the fuel pressure regulator if it is original. You could probably find a used one here in the parts forum. Please come back and let us know if this solves your problem.