Im sorry, but your question goes against the methodology of archaeology (and historical research). Researchers cannot prove a lack of something, only the existence of something.

This means, that when an archeological site of a neolitihic society us excavated, or ancient texts from the earliest civilisations are deciphered, we can only confirm (relatively speaking) that religion was practiced then and there in some form, or we can conclude that no religious leads were found. Whether the lack of religious paraphernalia/texts means that the culture was atheistic, or that we simply failed to find it, is up to debate.

The same principle is applied to other aspects of human existence. For example; we hardly ever find any proof that people in the prehistoric past sung songs. However, since neolithic whistles and flutes were found, it stands to reason that it might be possible that neolithic peoples enjoyed music, and might have made some of it orally.

The same could be said for religion; even when we don't find any temples, religious engravings or statues etc, we can reasonably conclude, looking at the comparable antropological evidence from other cultures, that people who bury their dead, and form communities large enough to require leadership, also developed some form of spirituality/religion to justify this behavior.

Another aspect you must take into consideration, is that "atheistic" means just "not believing in god(s)". It could be argued, that vast numbers of various animistic religions did NOT have a god/goddess, but rather worshipped elements of nature, thus were literally "atheistic", while still deeply religious/spiritual.

So in essence, when you ask if there were atheistic neolithic civilisations, the only answer a honest historian/archeologist can give you is ...maybe.

Sources:

Archaeology: Theories, Methods, and Practice- Colin Renfrew, Paul Bahn.

Hodder, Ian; Hutson, Scott - Reading the Past: Current Approaches to Interpretation in Archaeology

I just read a great book by J. Anderson Thomson, Jr, called "Why We believe in God(s)". It goes over some of the history and science that demonstrates the use of religion in early peoples as well as the development of segments of our brains that cause a greater connection to religious belief. Now he may be completely wrong but it was an interesting read. He also never pointed to an atheistic group, including in tribes with little modern contact.