God’s sovereignty over His creation is clearly established in Genesis 1. He is in complete control over the earth; everything happens at His command.
And then God makes man (and woman) in His own image. In Genesis 1:26 it’s very clear: He makes humans in His own image “so that they may rule.” The key here is that only God has license to rule. A created being cannot rule, unless it has something of God within it.
The created humans are given their very first instruction by God: “Be fruitful and increase in number; fill the earth and subdue it. Rule over the fish in the sea and the birds in the sky and over every living creature that moves on the ground.” (Gen. 1:28) The plants were given to the humans as food. (See Psalm 8:5-8)
So humanity had full dominion. God’s decree encompassed all that there was. And the first thing that the humans set out to do was to obey God, to take on this huge responsibility that He had given them. “The Lord God took the man and put him in the Garden of Eden to work it and take care of it.” (2:15) Man’s authority was demonstrated by giving him the right to name the animals (2:19).
All of this took place before sin entered the world. So it is clear that God’s entire purpose is expressed here. The dominion that was always His has been given over to the humans, who are to rule in God’s place, with His authority.
But when sin enters the world, the world is no longer wholly subject to God’s dominion. At that point, Satan becomes “the ruler of this world” (see Eph. 6:12, among many examples).
Because He has lost dominion, God’s purpose is now to get it back. Note: God has lost dominion, but He has not lost sovereignty. He is still all-powerful. He could conquer the evil and banish it altogether, and someday He will do that, but right now he wants the humans to retain the ability to rule and the free will to be able to make real choices.
For the rest of the Bible, God’s purpose is clear: win the people back to Himself. He wants dominion over the earth, yes, but most of all He wants dominion in our hearts.
“Turn to me and be saved, all you ends of the earth, for I am God, and there is no other. By myself I have sworn, my mouth has uttered in all integrity a word that will not be revoked: Before me every knee will bow; by me every tongue will swear. They will say of me, ‘In The Lord alone are deliverance and strength.” (Isaiah 45:22-24)