An inescapable judgement

I am reading through the Old Testament book of Ezekiel. One cannot escape the oft repeated phrase "Then they will know that I am the LORD". It occurs in the context of God's judgement on both Israel and her neighbours, for their sin (especially idolatry and injustice).
Thus, theology (which is the knowledge of God) cannot be separated from an appreciation (or experience?) of judgement.

How does this harsh picture relate to the New Testament?
Indeed, it is interesting that Jesus says in John 16 that the Holy Spirit will "guide you into all the truth" (v. 13) and

he will convict the world concerning sin and righteousness and judgment: ⁹concerning sin, because they do not believe in me;¹⁰ concerning righteousness, because I go to the Father, and you will see me no longer; ¹¹ concerning judgment, because the ruler of this world is judged.

On the cross, sin is judged and punished once and for all. Knowing this is the key to knowing the "I am" who is YHWH ("I am who I am").