340 starting issues

Have another carb like an Edelbrock 1406 to throw on it for a quick startup test?

Process of Elimination

Sounds like a plugged up fuel system/ plugged up carb.

Could be sediment in the carb, needs to be cleaned out.

How old is the fuel tank on the car, they do rust and scale up over time.

Fresh fuel filter?

Water condensation in fuel? Ethanol fuel draws moisture out of the atmosphere.