From the heavens you uttered judgment; the earth feared and was still, when God arose to establish judgment, to save all the humble of the earth. (Psalm 76:8-9 ESV)
God is the highest authority as Creator and Lord. When he speaks, all creation will stop and listen. For those who denied his existence, they will be terrified because their pride and arrogance steered them in the wrong direction. Their countenance will drop to a lowly state with their minds quickly regretting every word they spoke against Jesus and his followers, against God and his word, and against all the evidence they were provided of his divine reality. His countless invitations were ignored and they may never have another opportunity to accept it because they were preoccupied with their own ambitions, making and protecting a world where they cling to the value of independence. They did what was pleasurable to them, not caring if God called the acts and behaviors evil.
His judgments are final and there is no other appeals process because he is the Supreme Court; there are no other judges higher than him. Once he casts them, they will take their course and be fulfilled.
He will spare the humble, people who honored him, his Word, and his Son Jesus. His wrath will abate because they believed in him and his works. They walked in humility, expressed their love for him, and prayed that they would one day see him face-to-face. He became their God and their treasure, and therefore their judgment comes in the form of the ultimate reward: eternal life.