How was the birth date of the Prophet, peace be upon him, determined, given that the Hijri months were not used until after the Hijra, and is there a contradiction in determining this date, such as the differing opinions between the 9th and 12th of Rabi' al-Awwal?

The Prophet Muhammad (peace be upon him) was born on Monday, the ninth of Rabi' al-Awwal, in the Year of the Elephant, corresponding to April 20th or 22nd, 571 CE, according to the astronomical researcher Mahmoud Pasha. However, most biographers state that he was born on the twelfth of Rabi' al-Awwal. The discrepancy might be due to the Arabs' lack of precise historical record-keeping at that time. What is undoubtedly true is that he was born on a Monday in Rabi' al-Awwal, in the year of the Elephant incident. The lunar months existed before the Hijra, and the Hijri year began to be used after the Hijra. Allah Almighty says: "Indeed, the number of months with Allah is twelve months in the Register of Allah, the day He created the heavens and the earth; of these, four are sacred."