The fuel cannot evaporate out of the bowl of the carb because it is sealed in there by the float needle and seat. Here is what I think is causing the problem on these old machines with diaphragm style fuel pumps:
Diaphragm pumps have two reed valves that act as check valves so the pump can function. Also, when the machine is off, the reed valves hold the fuel in the discharge line and fuel bowl of the carb. Over the years, the reed valves get stiff, curl up, erode, etc., to the point where they don't seal well. This allows fuel to leak from the fuel bowl, through the reed valves and back to the tank when the machine is off. This is the root cause of the problem. With the fuel missing from the bowl and fuel line, the pump has to run for quite a while to restore that fuel during a cold start. This is made even more difficult because the pump isn't operating as efficiently as it would be with good reed valves in place.
The way to repair it is to either install a pump repair kit, which includes a new diaphragm and reed valves, or just buy a new pump. I don't know if either of those are available any more due to the age of the machine, though.