first thing to do is check that it is sealed and secured properly with tights nuts and gasket for the carbs, look for the obvious simple little things like loose, kinked, or cracked hoses and then look to the gas not getting there such as bloced water seperator filter or inside the engine cover fuel filter.
if the carb was rebuilt it can still have issues. it sounds to me like the gas isnt being let back into the float bowl. it starts and runs until it runs out of gas.
it could be the float needle is stuck or it wasnt put back together correctly, sometimes the clip comes off and the float needle never opens.
this goes on the premis that you have only one carburator but its not that likely this would be your problem if its got more then one carburator
you should be able to Idle it up by adjusting rod Cable should be just Bolt u screw in Hope it helps ya Marine Mech Aren't Cheap