John Niles in his book, Homo Narrans: The Poetics and Anthropology of Oral Literature gives voice to an emerging idea, namely that storytelling may be the single most important defining aspect of humanity. Regardless of where one places the craft of telling stories on the scale of humanity, it is clearly central to what the human experience is all about - and it apparently has been for a long time.

Folklore studies have applied some focus on the art of storytelling and its importance to people and their culture. These tend to be observations from more recent times - dating to professional collecting in pre-industrial people during the period of transition in the nineteenth century. That said, conclusions reached provide a means to gain insight into how storytelling likely manifested in previous times. Attempting to dig back to that primordial time "at the very beginning" when people "began abstract thought and began creating gods and stuff like that" - as you say - is not possible with written documents. It can only be imagined in abstract if not rather fanciful terms. If people like Niles are right, that storytelling is at the core of our humanity, we can imagine that the point when the practice emerged reached back hundreds of thousands of years, and one can only guess - without written records or archaeological evidence - how that process unfolded.

Following a brief excerpt from a book manuscript of mine that is currently under review. This is from a chapter dealing with historical forms of storytelling as perceived by folklorists; I offer it as a means to understand the sort of things that have been studied, in this case specific to Ireland where some of the best research has occurred:

Many societies also feature specialists who rise above the majority of active bearers of tradition. These skilled raconteurs graduate to the next level by becoming acclaimed and sometimes professional storytellers. James Delargy (Séamus Ó Duilearga; 1899-1980), the long-standing director of the Irish Folklore Commission, presented a classic study in 1945, addressing the nature of the seanchaithe, the storytellers of Ireland. His essay went a long way toward documenting the expert keepers of tradition who roamed the countryside, telling stories in exchange for room and board. Delargy was so eloquent and pathfinding in the field, that folklorists regard his work as the definitive early discussion about those who conveyed popular stories from one generation to the next.

A subsequent encyclopaedic study by Georges Denis Zimmermann is a twenty-first-century benchmark analysis of the Irish storyteller. Zimmermann draws on evidence from early material as well as from the later period of classic folklore collection in the nineteenth and early twentieth centuries. With this information, he is able to construct an elaborate portrait of those who told the stories. The insights of Delargy stand, but Zimmermann adds a comprehensive review of sources.

Delargy praised the conservatism of the Irish storyteller, suggesting that the craft, 'attained a very high degree of perfection in medieval times to judge from the detritus of the epic literature of the manuscript tradition which has come down to us from the eighth century. But the written saga is but a pale ghost of the tale that once was told, and the personality and polished artistry of the medieval story-teller can only be guessed at by the student of the written word who has not had the privilege of hearing the living voice of the modern reciter of Irish wonder-tales, the democratic descendant of the aristocratic story-teller of a thousand years ago.'He further suggested that there was ‘remarkable continuity of tradition linking the living oral literature of the Gaelic West… with that of the manuscript tradition in an unbroken chain of over 1,200 years.’

r/AskAnthropology might be a good place to ask this as well.