Possibly the cam ?

 

An air leak in the line between the pump and the tank will prevent the fuel pump siphon action from working fuel to the pump... or if the fuel line or the 'pickup sock' is clogged ? blowing air from the FP back thru the line to the tank might help you figure out the problem?

 

I would check everything from the sending unit suction strainer to the fuel inlet hose to ensure no blockage and/or air leaks are present.
I would be extremely careful blowing compressed air back into the fuel tank. The internal surface area will create quite a lot of force on the tank and could cause damage. If you blow air ensure the cap is off and blow with very little pressure. It would be best to disconnect the fuel line and remove the sending unit first to begin your testing.
Glenn

 

Does the pump pump out fuel itself? If so, you have something between it and the carb. Like the filter maybe? Does gas come out of the line where it attaches to the carb? Seems like it would be fairly easy to isolate.

On an old car that has sat for years with gas in the lines, I'd replace everything or at the very least, push some solvent through all the hard lines and blow them out.

 

Did you try pouring a little gas down the carb (put the air cleaner back on) and fire it up a couple times? Sometimes that allows the system to prime itself a lot easier.

 

55 Tony, I had just that problem on a variety of cars in the past. It seems once it gets started, the pump is able to pump faster to prime itself. I once had a 46 Willys Jeep (sold four years ago after owning it 30 years) and I had to run fuel down the line to the pump to prime to get it going eventually. A new pump solved that.