Ok so im wondering whether the choke solenoid is stuck and letting in excess air without letting in fuel is yours a manual or an electric choke/primer valve
Also a thought you said the carb was rebuilt was the float switch set correctly so only fuel enters the carb before the float pin engages I have known Air to enter with incorrectly levelling to floats in carbs
Check the woodruff key that adjoins the crank to the flywheel if the key is sheared the timing is out and the engine will not start at all, will just backfire here and there
