since atheist believes that gods don’t exist

This is a common misconception.

Theist is someone who believes God(s) exist(s).

An atheist is someone who does not believe God exists. They don’t need to have a positive belief of nonexistence of God.

Much like how a gnostic is someone who believes there is knowledge of the topic.

And an agnostic is someone who believes either they don’t have that knowledge or that the knowledge doesn’t exist.

So you could be an agnostic atheist (“I don’t know and I don’t believe either way in the absence of knowledge”) or an agnostic atheist (“I don’t know but I believe anyways”) or a gnostic atheist (“I know that they don’t and because I know I don’t believe”) or a gnostic theist (“I know they do and I believe because I know”).

Epicurus would have been an Agnostic atheist if we were categorizing. They ended up right about so much because they were so committed to not ruling anything out. They even propose that there might be different rules for different versions of parallel universes (they thought both time and matter were infinite so there were infinite worlds). It’s entirely plausible he would have argued for both the existence and nonexistence of gods in different variations of existence given how committed they were to this notion of not ruling anything out.

But it’s pretty clear from the collection of his beliefs that the notion of a god as either creator or overseer of this universe was not actively believed in outside of the lip service that essentially “yeah, sure, there’s gods in between the fabric of existence, but not in it.”

The Epicurean philosophy itself was very focused on the idea that the very notion of gods was making everyone sick, and that they offered their ‘cure’ for people to stop giving a crap about what gods might think or do.