There is no Inca writing. The dynastic past was held in knotted cord records and in memorised recitation maintained by the royal lineages, and each of those lineages had custody of its own founder's reputation, which is a system built to produce competing accounts rather than a single one.
What survives was written down after 1532 by people with interests. Juan de Betanzos lived in Cusco, spoke Quechua, and was married to a woman who had been a wife of Atahualpa, so his material comes through one royal lineage in particular. Pedro Sarmiento de Gamboa compiled his history in 1572 under the direct commission of the viceroy Francisco de Toledo, whose administration wanted to establish that the Incas had been recent usurpers and tyrants, since that conclusion made the Spanish conquest a liberation. Garcilaso de la Vega, writing in Spain from memory decades later, was the son of a conquistador and an Inca noblewoman and had an equally clear stake in the opposite direction.
None of these men is worthless and none can be read straight. The result is that Manco Capac cannot be treated as a historical individual whose dates or deeds are recoverable. Whether there was a founding figure at all, and whether the name belonged to a person or to an office at the head of a lineage list, are open questions.
What is recoverable is what the accounts were for. In every version the founder brings order, agriculture and law to people who lacked them, and stops at a place that becomes the centre of the world. That is a charter for an empire, told about its own capital, and it survived the empire by being written down by its conquerors.