The kingdom of heaven drawing near is the reign of God arriving in the Messiah’s ministry, then publicly vindicated when the rival administration falls.
In Daniel the kingdom of the God of heaven crushes rival kingdoms in history. John the Baptist and Jesus announce that that time has closed in — repent, because the reign is at the door.
Matthew 3 and 4 open the public ministry with the same sentence: the kingdom is at hand. Healings, exorcisms, and authority over Israel’s shepherds are not previews of a different kingdom. They are the kingdom attacking the old house.
A kingdom “at hand” in the 30s cannot be made “at hand” again as a slogan for every later decade without emptying the words. The first hearers were told to respond now.
The kingdom you enter is the one they said was near. It is not a second product still in development.