The word Atheis originates from word Άθεος (atheos). The word is composed from the Greek word for God Θεός (theos) and a- which means lack of something. So the lack of God is atheism (Αθεϊσμός in Greek) and the person that doesn’t believe in the existance of God/Gods is Atheos.
There is a debate between scholars if Xenophanes Kοlofonios or Diagoras of Miletus was the first atheist. The first one wrote critics to Isiodos about creating Gods with human bodies. It is closer of what we call today Agnosticism but it wasn’t easy someone to declare the non-existance of Gods in Ancient Greece. Diagoras of Miletus was sentenced to death but he avoided it by leaving the city.
Euripides or Critias wrote:
“the fear of the gods” in order to frighten people into behaving morally”
wikipedia
So even if Greeks were very open to new ideas the same time had also conservative societies that punished several times philosophers for being Atheists. One of them was Socrates.