I believe Jesus said to his disciples that all power was given to him in heaven and on earth after his victory at the cross. (Matt. 28:18) Didn’t this break the power of Satan and remove his “god of this world” title?
Paul called Satan the god of this age after the cross (2 Cor. 4:4). And 1 John 5:19 says “We know that we are children of God, and that the whole world is under the control of the evil one.”
The fact that John also wrote this after the cross tells us two things. First, being children of God gives us power to overcome the workings of the enemy. 1 John 4:4 says, “You, dear children, are from God and have overcome them, because the one who is in you is greater than the one who is in the world.”
Second, by saying that the whole world is under the control of the evil one (present tense), John indicated that although Jesus has been given all authority, He hasn’t yet begun to exercise it outside the Church. He won’t assume total control over Earth until the time of the end.
At the sound of the 7th Trumpet, which heralds the beginning of the Great Tribulation, loud voices in heaves proclaim, “The kingdom of the world has become the kingdom of our Lord and of his Christ, and he will reign for ever and ever.” (Rev. 11:15)
During the following 3.5 years He will systematically destroy all His enemies and return to Earth to establish His Kingdom here. In the mean time Satan is still running things, subject to a certain amount of restraint by the Holy Spirit. (2 Thes. 2:7).