Your bike has a magneto. The battery, rectifier and charge control (if original zener diode) have nothing to do with the motor starting or running. A healthy Atlas should not be terribly hard to start from cold (hot can be another matter). Do not give it any choke- the lever should be pulled into the "tight" position. Tickle the carb until some gas flows out of the tickler. Kick the bike while on center stand. If bike will not start after a 1/2 dozen solid kicks something is not right. FWIW I can't figure out your carb set up. An original '62 Atlas would have a single Monbloc or two Monoblocs with the right one being "chopped" with no float chamber. You seem to have "handed" Monoblocs - which was a later variation. You also have a Webco float bowl extension - a nice looking piece of questionable utility. Anyway there's nothing wrong with having a non original bike but it can complicate fault finding. If you continue to have difficulty it would definitely be helpful to have a knowledgable nearby person from the list look over the bike.