I have not checked FP cause I do not have a gauge......So I assumed initially the Floats were stuck like you mentioned....I cracked open the Edel and although the Float Level was lower, there was still fuel in the Bowels, enough that the Pump Shot should throw at least 10 to 15 shots, floats didnt appear Stuck Closed, they move freely, but it is difficult for me to imagine them being stuck closes (I did try tapping them at the beginning of my starting issues)....
so I had fired some compressed air through all the fuel systems in the carb, all bubbled or sprayed fuel through them.....after all that immediately after closing the lid and assembling, the pump shot STILL Didnt throw fuel......

Filter could be a problem and the screen in the tank, it is obviously possible but like I said everything is So New, would be odd for them to fail, plus the filter is a Larger Stainless container style......given all this, why does the car run and drive perfectly once, well, running???

I have similar, but not as severe, issue with 'cold' starts.  I believe my issue is that I need a check valve in the fuel line.  I have a Holley 650, double pumper; on cold starts, I pump the gas pedal once to the floor, and another pump about half way.  The engines starts, runs for a few seconds then stumbles a bit so I quickly oscillate the pedal just a bit several times to keep squirting fuel from the accelerator pumps (size 30cc size).  The engine smooths out and runs as it should on the choke. 
Seems to work for me, although I should install a check valve.
BTW - I don't think you'll 10-15 shots from your accelerator pump, from what I understand 3-5 full shots, w/o refills, is all you'll get.
 

How long since you last started the engine?
It sure seems to me that you had dry bowls.
 

Honestly if its after sitting for a while I just regard that as normal.  The fuel in the float bowl(s) evaporates out the vent(s).  Remember that system is not sealed.

TKO, when I cracked the Lid of the AVS2 it had fuel in it. Much of it did evaporate yes, but the Jets were immersed.
What I noticed was the PUMP Shot was throwing fuel.  Correct me if I'm wrong, but doesn't it get supplied from the bowels? 

Let's also keep in mind, once I drop fuel down, or, but some chance the car finds a way to stumble to start, after about 10-15s of rough start, it smoothens out and there is literally nothing wrong.
I'm really baffled by this, you'd think a fuel supply issue would rear it's ugly head during load.

M1Mustang69 wrote:

Everything New 3-4yrs ago.......MSD ignition system (no Box).....squirters squirt when/once engine is running.....it is literally after the car sits for a long period of time.....
 

This is normal after sitting for a long time. The fuel has evaporated from the bowls to a point where there is not enough fuel to start the engine. A long cranking session followed by a couple of pumps of the skinny pedal should work.

J3 pointed out his use of a electric fuel pump to combat this problem. I only have this problem on the first start of the year, after a winters rest, or if I've pulled the carb to work on it.

Yes, just because there is fuel in the bowl(s) doesn't mean there's enough to get it to start and stay running, especially if the line behind the carb is dry.  I find that for my car it takes about a week for this to happen.  When I drive it every day, or every coupe of days it lights right off, but if it sits for a week or more its not going to want to start without using the accelerator.