The First Strife is largely a theorized series of events, thought to have occurred sometime before recorded history. It is thought to be a period reminiscent of later Strifes, of near global war during which Primarchs were conquered, though the methods of combat would be far more primitive, consisting of copper and bronze age technology according to the few surviving relics of this time period.
If you were to pin a historian down (not a difficult feat, especially for an adventurer) they would readily admit that the First Strife is mostly a place holder, used to explain the “dark period” between Creation, and the antagonism by Primarch races during the events of the First Restoration. Without an established Antiarch society, the races of the Primarchs would have had no reason to rebel or to establish the city of Aecherron, which would serve as a sanctuary for the Primarch people for hundreds of years.
So by and large the First Strife is considered to be a period of imperial conquest by the Antiarch races, bolstered by their numbers and a proliferation of dragons, that set themselves as the rulers of Atlas. Though as any small child (provided they are a Primarch child) would be eager to tell you, that was not to last very long.