As I have had this happen twice (due to extended inactivity) I have looked at the fueling layout to see what the problem is. My opinion is that the fuel rail, which is located directly above the injectors, develops a vapor pocket which must be bled off before liquid fuel arrives at the injector inlet valves. The fuel pump/pressure sensor, which is back in the tank, simply sees fuel manifold pressure increase to the set point, and does not distinguish between a solid hydraulic line of gasoline and a vapor bubble which is being compressed by the pump. In other words, it is an open loop instead of a closed loop. So, as you have this vapor bubble sitting in the rail, above the injectors with a supply port on the on the bottom quadrant, the system is injecting unsaturated vapor instead of atomized liquid, at least to start with. As you continue to turn over the motor, the vapor bubble begins to deplete, replaced by liquid gasoline, but very slowly as the injection system is only dispensing a tiny bit of vapor each revolution. 10-20 seconds elapse and the rail begins to have liquid find its way to the injectors and it richens the mixture to the point that combustion starts to happen 1 cylinder at a time. Once it holds ignition on it's own, the purging completes itself and everything is back to normal.
I can't see a way to allow the fuel rail to self prime as the pressure relief valve is located inside the tank and you need to have a way to get liquid to flush through the rail. There is a pulsation damper on the rail but that need to remain to prevent hammering in the system from normal operation. Brazing a piece of tubing and installing a bleed valve would allow purging, but I wouldn't do that as it would be a safety hazard.