A couple of points:
1) The Alliance formed after a good chunk of the Galactic Empire was feeling the pressure of being imperial rather than republic. Granted, the republic was corrupt like Chicago during Prohibition, but while it existed many of the public departments were still actively serving their role (more or less).
2) The Alliance was not formed from the proletariat, but the noble houses and companies pushed out (who fell out of favor) when the empire rose. Their plan was to restore the republic system that recognized their wealth and political power. And there might have been a period like this comic when Imperial interests were willfully lying to opposition parties and interests to prolong the time before they got serious and formed a military.
3) It was atrocities like Alderaan that really fueled recruitment into the Alliance. Every young person who had family lost in the Alderaan event at least considered joining up, and if they were sympathetic to the Alliance (or had no loyalty to the Empire) were inclined to do so even if their prior ambitions were apolitical, e.g. art or medicine or civil engineering or whatever. ALSO Alderaan was only the most recent atrocity committed by the Empire in the name of enforcing its political power. And (as per long-studied Counter Insurgency) every act of brutality by tyranny draws more of the population into the resistance. The Alliance was just the most popular and best supported movement.
4) NOTE: This is speculation based on circumstances, much like the Endor Holocaust (The EH is implied by the ROTJ events but was later rectconned out via additional canon): The final point of the Death Star is not merely to be a planet-destroying superweapon but a mining tool to crack open (lifeless or evacuated) planets to get to interior precious minerals. While its success as such a tool might be uncertain, had it not been destroyed, the hope by its crew, engineers and support staff was that the superlaser would not often be used as a military device (optimally never again!) but could still be used in the process of gathering necessary resources.
