I would like to venture an opinion if I may. I believe God's kingdom is eternal. It has always existed, and it will have no end. So long as there has been God, so there has been a kingdom. This kingdom was extended to earth at creation, and Adam was given charge over it as God's representative, or steward if you like. Unfortunately, Adam switched sides, and presented this small piece of earthly acreage into the hands of the devil. God needed to take it back, and Jesus did so. This was accomplished at Calvar, as a matter of law, the earth now lagally once again is a part of God's kingdom, but it will not be as an experiential piece of God's property until Jesus returns as triumphant king.
I agree that it is eternal and agree that Eden was the kingdom of God, but the rest of the earth was under the rule of satan. This is why God chose man to grow and multiply, and rule over the earth, to take back the earth from satan, starting from the garden of Eden.
I believe that God is not interested in ruling and reigning over acreage only, but the souls of men and all the animals and plants also. It is the souls of men which changed from the kingdom of God to satan, and so did all the creation with man. Satan is the ruler of this world in the sense that he rules all human kingdoms, starting with Nimrod, the first ruler of a human kingdom. By default, the kingdoms of men are kingdoms of satan, which are opposed to the kingdom of God.
As you said, the kingdom of God is His reign from eternity to eternity. It includes from before the foundation of the world, the garden of Eden, the Old Testament patriarchs before the nation of Israel, then the nation of Israel, and the church in the new testament, and the coming 1000 year reign of Christ on earth, and the new heaven and new earth and finally the New Jerusalem for eternity.
The age we are in now is the age of the church, and this is how God's kingdom is manifested on the earth today. If someone were to ask "where is God's kingdom?", we could point to Heaven, and we could also point to the church (both invisible and visible). Obviously the kingdom of God is not any nation on earth today, but must be the church. By the word "church ", I mean a plurality of believers, not a particular organization or denomination. If we lived in the old testament times, and someone asked where is the kingdom of God, we would point to Israel. Of course I believe the church replaced Israel, and that there has been a succession of different ages from eternity to eternity, and other topics in this forum are devoted to this matter.