Do you prime it thoroughly before starting it? Possibly it's just some air bubbles in the long gas line back to the gas tank, either from a minute air leak somewhere or (more likely, in my opinion) from gas draining back to the tank eventually when the generator is turned off. On some generators, you prime by holding the switch in the off position for a spell (say 30 seconds, or by ear—you should hear the fuel pump operating).
It could be a fuel pump that's weak, too, though I think the more common symptom is that the fuel pump stops working properly when it gets hot rather than when it's cold.