A wrong understanding of what the Kingdom of God is will lead to a wrong view of how it "arrives", and therefore of when it arrives. During Jesus' time on earth, not only the Jews who were opposed to him misunderstood Messiah's role in establishing the Kingdom, his own disciples were confused by that. Even immediately after believing in the resurrection of Christ, the Messiah, they expected him to restore the kingdom to Israel - Acts 1:6.
The Big Problem initially was Jewish expectation of a restored, earthly kingdom with a human king reigning from Jerusalem. A second problem that causes confusion is what the word "arrives" means, in context of the Kingdom of God. There is a need to consider what it means for the Kingdom of God to be "present". A third point is the need to establish whether the Kingdom of God has ever been without its King - did its King ever relinquish his sovereign right to rule? Did he acquiesce to a usurper's claim to have the right to rule over the earth? From this, it also becomes clear that there's a need to establish who the King of God's Kingdom is.
Despite these important points, I'll stick to your basic question as to what Reformed theologians say about the arrival of the Kingdom of God, though it hardly needs to be said that not grasping what they believe about those related points will impact of any understanding of the question under consideration.
"It is easy to identify Christ's kingship exclusively with his
resurrection and ascension in glory. However, this misses the paradox
that lies at the heart of the kingdom he brings. In this age, it is a
kingdom of grace. The King's glory is hidden under the form of
rejection and suffering. At no point was Jesus without a kingdom even
in his ministry under the cross, and as we have seen, he is even now
'ever-living' at God's right hand to intercede for us. The crucifixion
itself can be seen as a kind of exaltation, as we find in the fourth
gospel: 'And I, when I am lifted up from the earth, will draw all
people to myself' (Jn 12:32). We might be inclined to think at first
to take this as a reference to Jesus' ascension, but the next verse
corrects that impression: 'He said this to show by what kind of
death he was going to die' (v.33). He is the 'brass serpent' raised in the wilderness, to that ll who look upon him will be saved (Jn 3:14
with Nu 21:8-9)... Even as he was hanging on the cross in dereliction
as the enemy of God and humanity, Christ was winning our redemption as
our conquering King.
"There is no tribunal so magnificent," Calvin wrote, "no throne so
stately, no show of triumph so distinguished, no chariot so elevated,
as is the gibbet on which Christ has subdued death and the devil.
(Commentary on Philippians-Colossians, 191, Grand Rapids; repr.
1979)...
Reformed as well as Lutheran theology has typically followed the
eschatological distinction of Christ's kingship between the reign in
grace (regnum gratiae) and his reign in glory (regnum gloriae).
God has installed his King on his holy mountain and now demands
universal homage [list of 13 scriptures]. But this kingdom is not
simply an extension or reinvigoration of the kingship in Israel, as
many of Jesus' admirers had expected..."
The kingdom of Christ, then, is in its present phase - before the
second advent - weak and foolish in the eyes of the world." Pilgrim
Theology, Michael Horton, pp214-6, Zondervan 2011
Don't forget, either, that the gospel accounts show Jesus to have been born on earth AS King (Matthew 2:2) so that even before his crucifixion he was rightly acclaimed as King (John 1:49 & Luke 19:38). Reformed theology often speaks of "The already/not yet" dialectic at work in understanding Christ's kingly office. It speaks of Christ's kingdom being present now (as it should be in believers who gain entry into it by the new birth) and the future consummation. It is a "semi-realized" kingdom. Christians live now in the tension between the kingdom's inauguration and its consummation when "the kingdom of the world has become the kingdom of our Lord and of his Christ, and he shall reign forever and ever" (Revelation 11:15).
