Another possibility is that the float chamber in the carb is leaking fuel, either externally or internally down into the manifold, while the car is sitting. When you try to start the car after a period of sitting, the mechanical fuel pump has to refill the empty float chamber, while cranking, before any fuel gets to the cylinders.
To check this, let the car sit for a day or two without starting it. Before you start it, remove the air filter housing and have someone pump the throttle while you look down the carb. If little or no fuel squirts from the accelerator pump jets, the float bowl has emptied while the car sat. A carb rebuild with a new float, needle and seat, and gaskets should cure the problem, if this is it.