No.
Genesis chapter 1 tells of the order in which things were created.Chapter 2 simply goes back and tells how and why he made man in chapter 1.
So many people think that there were two sets of man created.This is wrong however. Cain going over into Nod and taking a wife is one basis for this theory.
But listen,after God made man,they did not just run out and sin that very same day.On the contrary,they could have lived in Eden a million years before their fall.When God created them,he said,"Be fruitful and multiply".I am certain there were millions of people on Earth by the time of the fall.
Yet time as we know it did not start until after the fall of man.That is why the Bible truly starts after that point.And starts with Cain and Abel,being the first births recorded,after the fall.The Bible is about Man for Man and his relationship with God.