The idea of the Kingdom of God starts early in the Old Testament. Understanding what we are told in the Old Testament helps us understand the New Testament.
Right from the start, God wanted the nation of Israel to be His kingdom:
5 Now therefore, if you will indeed obey my voice, and keep my covenant, then you shall be my own possession from amongst all peoples; for all the earth is mine; 6 and you shall be to me a kingdom of priests, and a holy nation.’ These are the words which you shall speak to the children of Israel.”
The record says that King David and his son Solomon, occupied the “throne of the Lord” and reigned over the kingdom of the Lord:
5 Of all my sons (for the LORD has given me many sons), he has chosen Solomon my son to sit on the throne of the LORD’s kingdom over Israel.
23 Then Solomon sat on the throne of the LORD as king instead of David his father, and prospered; and all Israel obeyed him.
Because the Israelites didn’t want God as their ruler, the kingdom was destroyed by the Chaldeans:
15 The LORD, the God of their fathers, sent to them by his messengers, rising up early and sending, because he had compassion on his people, and on his dwelling place; 16 but they mocked the messengers of God, and despised his words, and scoffed at his prophets, until the LORD’s wrath arose against his people, until there was no remedy.
17 Therefore he brought on them the king of the Chaldeans, who killed their young men with the sword in the house of their sanctuary, and had no compassion on young man or virgin, old man or grey-headed. He gave them all into his hand.
But that was not to be the final end of God's Kingdom. The last king of Israel was told by the prophet Ezekiel that another king would one day sit on the throne he was about to loose:
25 “ ‘You, deadly wounded wicked one, the prince of Israel, whose day has come, in the time of the iniquity of the end, 26 the Lord GOD says: “Remove the turban, and take off the crown. This will not be as it was. Exalt that which is low, and humble that which is high. 27 I will overturn, overturn, overturn it. This also will be no more, until he comes whose right it is; and I will give it.” ’
Isaiah was one of the Old Testament prophets who foretold the coming of a king who would sit on David’s throne. This kingdom would be special as it will not end :
7 Of the increase of his government and of peace there shall be no end, on David’s throne, and on his kingdom, to establish it, and to uphold it with justice and with righteousness from that time on, even forever. The zeal of the LORD of Armies will perform this.
The prophet Daniel also said that God would set up a kingdom that would not end:
44 “In the days of those kings the God of heaven will set up a kingdom which will never be destroyed, nor will its sovereignty be left to another people; but it will break in pieces and consume all these kingdoms, and it will stand forever.