Nowhere in the New Testament are we told to "build the Kingdom of God" or to "expand it". Such talk is a failure to understand what the Kingdom is. And such a misunderstanding is likely what leads us to build empires in the name of God. From the examples of the first disciples, we are to:
– announce the Kingdom's arrival in Jesus (Acts 1, 8, 19, 20, 28) – help people receive it, i.e. enter it (1 Cor. 6, Gal. 5, Heb 12, James 2) – teach people to live in it (Matt. 5-7, Eph. 2, Col. 1) – call them participate in God's rule by making their places of domain reflect God's dominion– by loving and serving instead of dominating, by acting to end injustice, etc (1 Thess. 2, Rev. 5) – look for the culmination of the Kingdom when Christ returns. (1 Cor. 15)
Until we understand it, all that we do "for the Kingdom" will degenerate into human Babel-building towers.