Hard to start when cold

No choke doesn't help.. for my cars with no choke usually 2 pumps then crank and they fired right up.. BUT.. retarded timing makes a car a lot harder to start depending on how retarded. I would move it up just bit for testing and i would bet it fires up instantly...

Gas won't evaporate overnight btw... if you want to know for sure take off the air cleaner and pump the carb.. does it squirt? then it has gas in the carb..
Just because you bought a new carb, does not mean it has not been sitting on the shelf for a few years. No squirting would be an indentation to me the accelerator pump has dried out and needs to be replaced. The old leather pumps work better than the rubber ones of today. Using just ethanol fuel of today can be another issue. You can fine Un ethanol 93 fuel at some stations still. At least where I live. It does cost more.