The very fact that Adam and Eve sinned shows that the Law was already in existence. The Bible says that where there is no law, there is no sin (1 John 3:4 "sin is the transgression of the law" and Romans 5:13 "...sin is not imputed when there is no law").
There is another piece of Biblical evidence. God's Ten Commandments, as given on Mt. Sinai, includes a command to "Remember the Sabbath Day". The "Sabbath Day" is a memorial of God's creation of Earth and was the beginning of what we know today as the "Sabbath". The account of how this special day came to be is found in Genesis 2:1-3, "Thus the heavens and the earth were finished, and all the host of them. And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made. And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made."
As you can see, the Sabbath was not given to the Jews only, but to all humans clear back at Earth's creation. God tells us why He created a special day, "because that in it he had rested from all his work which God created and made." This special day was actually a "Birthday" or "Memorial". (For further study, read The Literal Week)
The Bible also shows that God's Law existed even before the world was created. The fact that Satan sinned shows that the Law already existed in Heaven. Remember that the Bible says that "sin is the transgression of the law". When Satan sinned he broke God's Law.
God's Law was summed up by Jesus when He said, "Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the first and great commandment. And the second [is] like unto it, Thou shalt love thy neighbour as thyself. On these two commandments hang all the law and the prophets." (Matthew 22:37-40) God does not change, neither does His Law change.
See: The Ten Commandments of God