Often Scripture does not use the same rules for imagery or names of things which we use in modern times. For instance, in talking about the kingdom being established. On one hand it talks about the kingdom being established in the days of the Roman Empire in places like Dan 2:44. The passage is clear, but you have to look at the preceding context.

Then in the days of the Roman Empire, John the Baptist and Jesus came teaching that the kingdom of God, the kingdom of heaven, was at hand, Mtt 3:2, Mtt 4:17, etc. This made a great deal of sense in terms of Dan 2:44, and other passages like the seventy sevens of years in Daniel 9.

Following the events in the gospels it speaks of the kingdom as being in existence. For example,

“who delivered us out of the power of darkness, and translated us into the Kingdom of the Son of his love;”
Col 1:13

That is clearly past tense, He has “translated us in the Kingdom.”

On the other hand, there are many passages
which speak of the kingdom as having
already been in existence.

For instance in Ephesians 2 it speaks of us Gentiles in the flesh, called “uncircumcised,” by those circumcised in the flesh, Eph 2:11. Before Jesus came it says of us gentiles,

“that you were at that time separate from Christ, alienated from the commonwealth of Israel, and strangers from the covenants of the promise, having no hope and without God in the world.”
Eph 2:12

It talks about us Gentiles (those of the nations, from ethnos or nation) as being separated from “the commonwealth” politeia, which is the word for a citizenship, a community, and city or kingdom; which is of Israel ! The root word is polis which means a city or a town. We get our word “politics” from these words, and our word for city law enforcement, that is the “police.” This is talking about a political unit that Gentiles used to not be a part of. But now,

“… you are no longer strangers and foreigners, but you are fellow citizens with the saints, …”
Eph 2:19

It includes all Jews and Gentiles in Christ. And there are many other passages like this.

So what is the answer?

The coming of the kingdom is talking about the reign of the Messiah, the special one who would bring a reign of peace. It is talking when the rule of the Christ would start. It started after Jesus death, so Jesus says,

… “All authority has been given to me in heaven and on earth.”
Mtt 28:18

So the reign of the Messiah started in the first century AD. Now it is being fulfilled when it says to Him, “… Rule in the midst of your enemies,” Psa 110:2. He NOW rules in the midst of His enemies,

“For he must reign until he has put all his enemies under his feet. ”
1Cor 15:25

That process is going on now, and will be completed at the Second Coming. Then the Messiah will deliver the Kingdom up to God, 1Cor 15:24

Scriptures are from the World English Bible (WEB), a copyright free revision of the original ASV American Standard Version 1901