Here is something to check for it may not be the engine but in the wiring of what is is used on. Check for power at the fuel solenoid at the carb. It may not be getting power on start up and the engine has to come up the speed for the solenoid to get power from the charging system for it to start. I see this happen on a Kohler before. It turned out to be a bad key switch. Good luck.
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