There has been some recent press about the “Birmingham Quran”, which carbon dating suggests may pre-date the Prophet Muhammad, at the very least suggests the Quran was written down long before the mainstream view.
The traditional Sunni view is that the Quran was mainly recorded orally with a few verses written down with some companions. Sunnis go on to say it was written down during Uthman’s time, and then the text became standardised. This theory would date the Quran to be around 655.
According to this article, the carbon dating of a Quran was found to give it a date of 568AD and 654AD, suggesting this is either one of the very first Qurans ever written (highly unlikely), or that there were many Qurans written by that time and in fact the Quran had been written earlier, perhaps even during the life of the Prophet SAW.
The Shia view is that the Quran was compiled by the Prophet SAW in his lifetime which is from approx 570-632.