We can go as to
meaning ‘a universe without God’ which is another way of saying ‘God does not
exist’ , affirming the non existence of God.
You're still projecting the modern English noun usages (i.e. With the endings "ist" and "ism") backwards upon the Greek adjective.
"It is only about a decade after Socrates' death, in Plato (ca. 429 - 347 B.C.) that we start to find the Greek word atheos, which originally was used in the meaning, "godless, without gods, godforsaken," denoting intellectuals who denied the gods of the city or any form of deity." -Martin, Michael The Cambridge Companion to Atheism p. 19
"Atheism and atheist are words formed from Greek roots and with Greek derivative endings. Nevertheless they are not Greek; their formation is not consonant with Greek usage. In Greek they said átheos and atheotēs; to these the English words ungodly and ungodliness correspond rather closely. In exactly the same way as ungodly, átheos was used as an expression of severe censure and moral condemnation; this use is an old one, and the oldest that can be traced. Not till later do we find it employed to denote a certain philosophical creed." -Drachmann, A.B. Atheism in Pagan Antiquity (Emphasis mine)