Here is the original fragment regarding the "birth" of the Emperor first described in the "Realm of Chaos: The Lost and the Damned" in 1990:
The Emperor was born while the rhythm of the warp still flowed strongly through all natural things. The old shamans were guided by the warp and in their turn guided their people. But even then the growing power of humanity was beginning to make itself felt, and the shamans feared that their knowledge and whole way of life would eventually pass away. The energies they depended upon were becoming increasingly difficult to tap. Worst of all, they were losing the ability to reincarnate. For as long as anyone could remember, when a shaman died his soul had flown into the warp and bathed in its energies, awaiting renewal in another body. Now, the souls were being best, chased and consumed by the malignant Chaos Powers. Terrified for the future of their race, all the shamans of Earth gathered in one place and began the longest and most important debate in the history of humanity, lasting centuries and leading to the birth of the New Man.
After hundreds of years of debate and research the Shamans came to the conclusion that they were doomed, and that without them the whole race would soon fall prey to the psychic entities it had created in the warp. At the same time the disruption of the natural rhythm of the warp would result in the inevitable decline of the whole planet. They divined a future when all of creation would be consumed by mankind’s greed and ambition.
Although their own power was still strong the shamans realised that they could survive for only one or two further incarnations. They were not men to accept death easily. Many of them could remember the dawn of their race, when in other bodies they had walked under African skies. Having survived so long, for millions of years, it was not their way to die without hope or purpose. They therefore decided to pool their own energies by reincarnating in a single body. In their thousands they swallowed poison, and in their thousands they died, and their kind was gone from the earth.
Within a year the man later to be known as the Emperor was born. As he grew older his powers began to manifest themselves and he gradually remembered the thousands of lives that lay behind him. He was the New Man. But he was also the past. His powerful mind could still sift the natural energies of the warp, enter the lives of plants and animals, promote harmony, and ease the suffering of others. And he remembered how he was made to live forever, so that he would never have to reincarnate, but would survive unchanged for eternity. At last he remembered everything that had led up to his birth, and he left his own people to begin his endless journey around the world and through human history.
Since then a new story has been described in the "Master of Mankind" by Aaron Dembski-Bowden, that describes Emperor as a human child that has awakened his powers when he finds that his uncle has murdered his father, which could have been the first murder committed by a human with cold blood (the first murder has been described in the book, but it is unclear are those the same murders). Emperor shows this vision to Ra, one of his Custodes, but then the same story can be a metaphor since Emperor doesn't respond to the outright question "Did this truly happen?"
This doesn't negate the shamans' origin story - the "Master of Mankind" version simply says that Emperor was a child at some stage and his father (real or adopted) has been murdered and "the boy who will be king" was able to stop the heart of the murderer.
Both of those origins date his birth to around 8000 BCE and place it in Anatolia (modern day Turkey).
In the afterword to the "Emperor of Mankind" the author says:
I didn’t want to reveal anything about the Emperor as any kind of definitive, objective truth. I don’t think anyone should, either - partly because understanding the Emperor’s nature and origins hasn’t been important for three decades of enjoyment in the supremely popular setting (and it’s never going to be necessary for that), and partly because, well, no answer will ever be satisfying enough or believable enough for everybody. [...]
Could the Emperor have been born from the souls of primitive shamans? Is he a Dark Age construct aping human form, left out to enact his will over the now-ignorant species? Was he a manipulative overlord and tyrant who knew everything of Chaos? Was he just a good man whose intellect strained to work alongside the levels of those beneath him, and was he ultimately failed by lesser beings?
All of them might be true. None of them might be true.