Atheism is doubting and questioning the existence of a god and by extension, religious practises though it has undergone changes given the context it’s in. But there were atheists in the classical period, like Diagoras of Melos who publicly exposed certain rituals and practises in addition to denouncing it. Keep in mind that this wasn’t the first time atheists tried to explain scientifically.
What came close in the Hellenistic period were philosophers that tried to explain things scientifically instead of superstitiously like what most people did and arguably still do if you replace Greek polytheism with Hinduism, Shintoism or whatever. (There probably was another Greek who said that the universe revolved around the Sun and another said that the Sun’s a star but I forgot whoever said that.)
The biggest salient difference between old atheism (classical atheism if you will) and new atheism is that the former’s philosophically rooted and the latter’s scientific. It’s unsurprising that historically some of the most well-known atheists were philosophers. And that skeptics dislike philosophy, which is ironically how atheism started.