Have you also tried priming the fuel filter before starting just in case it's a fuel starvation issue?
Hello. You referring priming it manually ? If that is what your are asking than no. Because the car runs once it starts, I presume there can be no issues with the fuel filter. I had it replaced 6 months ago. It's a quality fuel filter.
I always let the fuel filter light go off before turning the ignition . Also the glow plugs indicator. In fact, 2 times I've turned the ignition and let it crank some many times, I ran out of battery voltage at some point lol. Had to "borrow" some power from a friend's battery using cables. Made sure he'd stick around

I also tested the injectors. 2 of them had to be reconditioned cause they failed the fuel return test. They were returning fuel 2 times faster than the other 2. I've got the control valves changed thinkin' this might resolve my issue but it didn't. After the change, I got worried cause right after I left the service shop, I had some unusual vibrations on idle (I felt it on the driver seat). Also, the vibrations were slightly perceivable when I was accelerating the car between 1000 and 1500 rpm. Drove it like that like 5 km the and both vibrations disappeared. I guess it was an ECU adjustment to the 2 injector valved changes ? I don't know.