Joh 3:3 Jesus answered and said to him, "Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God."
It means to participate in the kingdom and experience it. It's talking about experiential knowledge.
Notice how the Lord shifted from knowing God and seeing God:
Joh 14:7 "If you had known Me, you would have known My Father also; and from now on you know Him and have seen Him."
Joh 14:8 Philip said to Him, "Lord, show us the Father, and it is sufficient for us."
Joh 14:9 Jesus said to him, "Have I been with you so long, and yet you have not known Me, Philip? He who has seen Me has seen the Father; so how can you say, 'Show us the Father'?
If Philip experienced the Lord Jesus Christ by being His disciple all this time then he has seen or known the Father in Christ Jesus. He experienced God in Christ.
And so, seeing the kingdom of God is participating and experiencing the kingdom. No one can enter and therefore experience the kingdom of God if one is not born again.