No One Gave the World to Satan
Adam did not hand the earth over to satan. Yahweh did not hand the earth over to satan. Satan said to Jesus in the wilderness that authority and glory over all the kingdoms of the earth had been delivered to him, and offered those things to Jesus (Luke 4:6). There is no Scripture indicating that he wasn’t lying. He is always lying. After He gave the earth to the domination of Adam, Yahweh gave it to Noah.
For clarification, imagine a playground that has 40 8-year-old children on it every day during recess at school. 3rd graders. There are two bullies in the crowd who don’t like each other. They each have 4 children who follow them and help them terrorize the other children. They steal food and money from other children. They hurt children who resist them.
When the timid children submit to the bullies, obeying them out of fear, they have not changed the playground rules. The rules could be enforced by the teachers who should be watching the activities during recess and the bullies could be detained and punished. The timid children have not given the playground to the bullies. They don’t have that much ownership of it. They are only giving them their property and their obedience. At playground level, and at school level, nothing has changed regarding the rules or the ownership.
In the earth, the Hindus can give what they own to demons they fear and worship. The Marxists can give what they can steal from people who work to whomever the Marxists serve. The Muslims can give what they work for or steal to their moon god. They can only give the unclean spirits what they can get control over, though. No one has given satan the earth. All of humanity would have to agree on it.
Satan does have power over the parts of the earth where his servants live, but he doesn’t have authority over any of it. Just power. He has that over anyone who lets him have it. Just like the bullies are pretending they own everything on the playground, they can’t even agree between themselves that it is true regarding the other. One says he owns it all, the other says she owns it all. Neither one owns any of it.
Jesus has been given all authority in Heaven and on earth, because when He became a man He added human authority in the earth to the authority He already had in Heaven (Matthew 28:18).