A man called Willard F Libby pioneered it at the University of Chicago in the 50's. This is now the most widely used method of age estimation in the field of archaeology.
What this means is that when you read some extraordinary claim you should be extraordinarily suspicious, at least at first.
First off, the purported variations were reported to be cyclical.
So the net effect on archeological dating would be null even if these variations existed.
The Greeks consider the first Olympic Games as the beginning or 776 BC.
The Muslims count the Prophet’s departure from Mecca, or the Hegira, as their beginning at AD 662.