There are a few more possibilities:
All modern engines with electric start and a charging system have a fuel shutoff solenoid mounted in the carb and most if not all have a plunger that closes off the high speed jet when power is off. There is a possibility of a fuel leak at this solenoid, or the solenoid is not functioning correctly. It should fully retract when power is turned on at the key switch.
Another possibility is that the float level may be too low.
And there is also a possible air leak somewhere in the engine intake system.
I'm not familiar with Kawi engines but many newer engines have plastic intake systems which increases the probability of cracks. There could be a gasket missing or not correctly installed.
I would also do a cold engine spark check to see if spark is there at first cranking of the engine.
If my Scag Tiger Cub sits for three weeks or so and not used due to weather, it has an extended cranking period before starting, B&S engine. I now use a fuel additive called Sea Foam which with regular use has solved the stale fuel problem. If you are in an area where the gasoline has 10% ethanol, then the fuel can be a problem.
If you engine is still under warranty then I suggest that you find a quality Kawi engine servicing dealer and chat with them about your starting problem.
Condition of the air filter???