Gotta disagree. I am a hardcore atheist but I fail to see how atheism is supposed to solve any problems. You could even claim that such an attitude would be religious again..
Trek seems to say it was not so much that atheism solved our problems, it's the result of atheistic attitudes that solved the problems.
An atheist won't waste time praying or performing rituals, to create a better future. Instead they use their intelligence, technology, planning and so forth to create a better future.
Take Devil's Due From TNG for example;
PICARD: Did Ardra simply snap her fingers, transforming Ventax Two into paradise?
JARED:The changes occurred gradually,over a long period of time.
PICARD:Did she personally form the government that has peacefully ruled Ventax Two for a millennium?
JARED:No, historical records indicate a council was convened to assessour options. They drew up a new constitution which the populationlater ratified.
PICARD Did Ardra pick up even one piece of trash?