Hyborian Age

Know, O prince, that between the years when the oceans drank Atlantis and the gleaming cities, and the years of the rise of the sons of Aryas, there was an Age undreamed of, when shining kingdoms lay spread across the world like blue mantles beneath the stars

The Hyborian Age is the fictional era created by Robert E. Howard in which the stories about Conan take place. In his essay "The Hyboran Age", Howard describes this as the time between Atlantis sank in the ocean and the rise of the ancient civilisations we know from history.

Placement of Conan Exiles
According to the developers, Conan Exiles is said to take place between the events in "The Slithering Shadow" (also know as "Xuthal of the Dusk") and the novella "A Witch Shall Be Born". While the time between these stories - and sometimes even the order of which they happened - are presented differently, it's most commonly said that "The Slithering Shadow" came before "A Witch Shall Be Born". Conan is around 30 years of age at the time of "A Witch Shall Be Born", which places Conan Exiles at least a decade before the events in "Age of Conan".