hi
not posable for fuel to go back to pump after it enters the carb !
you eather have a fuel evaporation problem due to heat or you have a internal leak in the carb allowing the fuel to leek into the intake and cylinders !
what carb do you have ?
Don't waste your money on a new pump
Agree the pump is likely fine... especially if it runs OK after starting. Fuel evaporation is very likely. I have switched my carb vehicles to electric pump for this reason. Key on for a few seconds re-primes the system and starts right up. This also can eliminate vapor lock.