Earlier I quoted the passage at the beginning of Mark where Jesus proclaims the kingdom:

Now after John was arrested, Jesus came to Galilee, proclaiming the good news of God, and saying, “The time is fulfilled, and the kingdom of God has come near; repent, and believe in the good news.”

Elsewhere in the Gospels Jesus makes an argument for this:

Then they brought to him a demoniac who was blind and mute; and he cured him, so that the one who had been mute could speak and see. All the crowds were amazed and said, “Can this be the Son of David?” But when the Pharisees heard it, they said, “It is only by Beelzebul, the ruler of the demons, that this fellow casts out the demons.” He knew what they were thinking and said to them, “Every kingdom divided against itself is laid waste, and no city or house divided against itself will stand. If Satan casts out Satan, he is divided against himself; how then will his kingdom stand?  If I cast out demons by Beelzebul, by whom do your own exorcists cast them out? Therefore they will be your judges. But if it is by the Spirit of God that I cast out demons, then the kingdom of God has come to you.

This argument does not prove that he is casting out demons by the Spirit of God. The argument is that if Satan is casting out demons, then his kingdom cannot last, and therefore the kingdom of God is coming. Likewise, if God is casting out demons, then the kingdom of God has come. Either way the kingdom of God has come near.