This depends on your definition of 'refugees'.

In 1951, a convention was held in Geneva to give an official definition to the term, and from henceforth it was possible to declare whether a person was a refugee or not. [source: UNHCR official site ]

However, before that there were already large population movements caused by war, famine and other forms of destruction which would cause the peoples' homeland to be inhospitable to them.

In China, one of the earliest records of such a wide scale immigration would be during the spring autumn period, when the Yue 越 king Gou Jian 勾践 destroyed the Wu 吴 kingdom. Due to the demeaning treatment that he had suffered under the Wu king previously, Gou Jian was determined to eliminate Wu utterly. Therefore the Wu people were forced to cross the sea to the Eastern islands, which is now modern day Japan. Future contact between the Han dynasty and the Japanese islands state that the Wa 倭 people claimed direct descent from king Taibo 泰伯 of Wu, and often spoke with a Wu accent and adhered to Wu customs, further supporting the theory of them being former refugees of the Chinese Wu. [source: the Book of Han 汉书, Discourse on Balance 论衡]

Although the term refugee isn't used, there are a number of places where peoples 'seeking cities / lands of refuge' are referenced in the Bible - whether that has merit as a historically accurate source or not, it is still a historic text in terms of age, and definitely alludes to the concept of refugees.

Here is one example (to fit more in with the common modern concept of refugee, I have selected an example of mass movement of peoples due to war / civil instability):

Exodus 12:37-39 "Now the sons of Israel journeyed from Rameses to Succoth, about six hundred thousand men on foot, aside from children. A mixed multitude also went up with them, along with flocks and herds, a very large number of livestock. They baked the dough which they had brought out of Egypt into cakes of unleavened bread. For it had not become leavened, since they were driven out of Egypt and could not delay, nor had they prepared any provisions for themselves."

I think this qualifies, since your question is phrased to the concept of refugee, and not 'the first historically bulletproof accounts of actual refugee events'. :)