The OT did not find the term kingdom of God or kingdom of heaven. However, the idea was there, at least as a type and shadow.
God spoke to Moses in Ex 19:
David spoke in 1 Chronicles 28:
Solomon was the earthly king, but the LORD was the heavenly king over Israel.
Isaiah prophesied in 9:
Daniel broadened the prophecy in 7:
In the NT, Jesus introduced his concept of the kingdom of God, bright and early in his ministry in Mark 1:
No, not really, but yes, as a type and shadow pointing to the true Kingdom of God in the NT.
God spoke to Moses in Ex 19:
The Israelites were meant to be a holy nation with the LORD as king. But they rejected him. 1 Sam 8:5 "Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine; 6and you shall be to me a kingdom of priests and a holy nation.’ These are the words that you shall speak to the people of Israel.”
They wanted an earthly king over them like other gentile nations.7 And the LORD said to Samuel, “Obey the voice of the people in all that they say to you, for they have not rejected you, but they have rejected me from being king over them.
David spoke in 1 Chronicles 28:
I.e., the geopolitical kingdom of the unified Israel before it was divided.5 Of all my sons—and the Lord has given me many—he has chosen my son Solomon to sit on the throne of the kingdom of the Lord over Israel.
Solomon was the earthly king, but the LORD was the heavenly king over Israel.
Isaiah prophesied in 9:
Jesus fulfilled Isaiah's prophecy. The kingdom is a spiritual one. Jesus called it the Kingdom of God (Kingdom of Heaven).6 For to us a child is born, to us a son is given; and the government shall be upon his shoulder, and his name shall be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. 7 Of the increase of his government and of peace there will be no end, on the throne of David and over his kingdom, to establish it and to uphold it with justice and with righteousness from this time forth and forevermore. The zeal of the LORD of hosts will do this.
Daniel broadened the prophecy in 7:
Jesus is the king of this spiritual and universal kingdom.13“I saw in the night visions, and behold, with the clouds of heaven there came one like a son of man, and he came to the Ancient of Days and was presented before him. 14 And to him was given dominion and glory and a kingdom, that all peoples, nations, and languages should serve him; his dominion is an everlasting dominion, which shall not pass away, and his kingdom one that shall not be destroyed.
In the NT, Jesus introduced his concept of the kingdom of God, bright and early in his ministry in Mark 1:
Was Jesus' Kingdom of God present in the OT?15 and saying, “The time is fulfilled, and the kingdom of God is at hand; repent and believe in the gospel.”
No, not really, but yes, as a type and shadow pointing to the true Kingdom of God in the NT.