It will advance mainly by the operation of the Spirit in the lives of increasingly sanctified, law-keeping Christians who practice their Faith in family, work, school, church, and all areas of their lives. Fathers inculcate the orthodox Christian Faith into their families. Pastors lead their flock into greater obedience. Educators instruct their pupils in terms of a comprehensive Christian life-system. Churches revive the diaconate and care for the sick, the needy, the widow, the orphan.
Entrepreneurs create wealth by starting new businesses that benefit others.
And on and on in all spheres. To surrender politics, or any other legitimate sphere of Christian activity, to the Devil and his disciples is an evil tack. But establishment of an explicitly Christian state will be the effect of broadly based Christian faithfulness beginning with the regenerated individual and family and reformed church. Christ's kingdom is less externally spectacular than earthly kingdoms, just as his birth was less externally spectacular than merely human kings' births. Christ's is a quietly and unobtrusively advancing kingdom.