Wouldn't evil have already existed on Earth before Adam and Eve? We all know the story of Adam and Eve causing the first original sin by eating from the Tree of Life. However, Lucifer became Satan before Adam and Eve were even created, he was casted down to Earth as described in Ezekiel 28:18. It is assumed that the serpent described in Genesis is Satan, right?

Wouldn't evil have already existed on Earth before Adam and Eve? If Adam and Eve were the ones who cursed the Earth from their disobedience, then would that mean Satan performed no evil on Earth before Adam and Eve? It seems rather confusing. If Satan did commit evil before Adam and Eve's arrival, then wouldn't the Earth have already been cursed?
Earth was created specifically with men in mind. Adam and Eve were given dominion over all the creatures over the earth. 


  And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth. (Genesis 1:26)


Therefore when man fell, the earth and everything under their dominion fell as well. Satan was permitted on earth to test them, but the earth was not cursed until men betrayed their allegiance to God. And even then, in a sense, God cursed the earth for our sake, since idleness can easily lead to temptations for a sinner. 

Therefore Satan was an usurper of Adam's dominion, he is referred to as "the prince of this world" (John 12:31). However, this dominion was never Adam's to give away, it rightfully belongs to God. As soon as man sinned, the plan of salvation was put in place (Gen 3:15). The earth, although under the curse of sin, was flooded with grace (Rom 5:20). Because Jesus, "the lamb slain from the foundation of the world" is the rightful ruler.