Is there a historical record of the calendar system that the Arabs in Mecca and Medina followed before the prohibition of Nasi' (intercalation)?

Al-Nasi' is the act of making a sacred month profane and making another month sacred in its place, which is what is mentioned in the Almighty's saying: (Indeed, al-Nasi' is an increase in disbelief). The Arabs before Islam relied on the lunar year of 12 months and designated four sacred months for fighting. They did not have a specific unified calendar; rather, they dated events by important historical occurrences such as the building of the Kaaba, the Year of the Elephant, and the Fijar War. They used names for both lunar and solar months, and these names changed and were unified a period before Islam.