Kingdoms usually advance through wise strategy, earthly conquest, war, and power.
At the present, God's kingdom advances through teaching, prayer, service, and love. At Christ’s return, God will judge the nations; but for now God extends mercy and grace to anyone who comes to him.
Jesus brought an other-worldly kingdom to earth (John 18:33–37). Jesus’ kingdom advances through the preaching of the gospel, the administration of the sacraments of Baptism and the Lord’s Supper, and the discipleship of believers (Matt. 28:16–20). Jesus’ kingdom is characterized by humility and grace (Matt. 5). The warfare waged by this kingdom is spiritual, using faith, arguments, and prayer (2 Cor. 10:5; Eph. 6:10–20). Furthermore, this kingdom appears as weakness (1 Cor. 1:18–31).
When Jesus taught his disciples to pray, one of the things he taught them to request of the Father was, “Your kingdom come, your will be done, on earth as it is in heaven” (Matt. 6:10).
There is a lot here on earth to pray for: the church's mission, mercy, grace, holiness, obedience, and Christ's return—to name just some things.
The temptation is to take matters into our own hands and to try to use our good ideas to advance God's kingdom. We want to do something new, something appealing, or something more dignified; but Jesus tells us to pray.