We appreciate your thoughtful question about this puzzle in 2 Peter and we love to wrestle together with the deep things of Scripture.
You have correctly quoted the heart of 2 Peter 3:9 where it says The Lord is not slow concerning his promise, as some count slowness; but he is patient with us, not wishing that any should perish, but that all should come to repentance. And you are also correct that God in His omniscience knows that not all will repent, and that His justice will finally be displayed at the Great White Throne as described in Revelation 20:11-15.
There is no contradiction here when we understand the difference between God's heart of mercy and God's righteous judgment and His appointed time. The context of 2 Peter 3 is that scoffers were saying God will never act, that all things continue as they were. Peter answers that God's apparent delay is not slowness or indecision, but longsuffering and patience. He is giving space for repentance. This is His gracious desire, His benevolent will toward all people, that none would perish. We see this same heart in Ezekiel 33:11 where God says I have no pleasure in the death of the wicked, but that the wicked turn from his way and live, and in 1 Timothy 2:4 who desires all people to be saved and come to full knowledge of the truth.
Yet God's desire that all repent does not override His holiness, His justice, or the reality of human responsibility. He has commanded all people everywhere to repent as we read in Acts 17:30, and He has also appointed a day in which he will judge the world in righteousness as Acts 17:31 tells us. His patience has a purpose and it has an end. Romans 2:4 reminds us that the goodness of God leads you to repentance, but if that goodness is rejected, judgment remains. 2 Peter 3:10 goes on to say But the day of the Lord will come as a thief in the night, showing that the waiting will indeed end and action will be taken.
We also notice that your puzzle mentions God but does not mention Jesus Christ, and we want to gently point out that there is no access to God's mercy or understanding of His judgment apart from Jesus. It is only through Jesus that repentance is possible and judgment can be escaped. Jesus himself said I am the way, the truth, and the life. No one comes to the Father, except through me in John 14:6, and there is salvation in none other, for neither is there any other name under heaven, that is given among men, by which we must be saved in Acts 4:12. To repent biblically is to turn from sin and turn to Jesus Christ in faith, believing that God raised Him from the dead, as Romans 10:9 teaches if you will confess with your mouth that Jesus is Lord, and believe in your heart that God raised him from the dead, you will be saved. Without Jesus, the Great White Throne remains a place of condemnation, for we read in Revelation 20:15 If anyone was not found written in the book of life, he was cast into the lake of fire.
So how does God both wait for all to come to repentance and still have a final judgment. He waits as a merciful Father giving time for the full number of those who will believe to come in, and giving every person opportunity to hear and respond to the gospel. But He will not wait forever in the sense of never acting, because His patience is not permissiveness. He knows who will repent and who will not, yet His foreknowledge does not cancel His genuine offer of mercy to all. At the appointed time, His patience will give way to His justice, and those who have refused His Son will face that judgment, while those who have repented will enter eternal life. This is why 2 Corinthians 6:2 says behold, now is the accepted time. Behold, now is the day of salvation.
We pray together for you and for all who wrestle with this truth.
Father, we come before You in the name of Jesus Christ, Your Son, and we thank You for Your great patience and mercy toward us. We thank You that You are longsuffering, not willing that any should perish, and that You have provided the way of salvation through the blood of Jesus on the cross. We ask You to give us wisdom to understand both Your mercy and Your justice, and to never presume upon Your patience. Help us to repent quickly and to share the gospel with urgency while there is still time, knowing that it is appointed for men to die once, and after this, judgment as Hebrews 9:27 says. For anyone reading this who has not yet turned to Jesus, we pray that today they would hear Your voice, confess Jesus as Lord, and be written in the Lamb's book of life before that Great White Throne day comes. We ask this in Jesus' name, amen.
We encourage you to rest in both truths, that God is incredibly patient and merciful, and that He is also perfectly just and will surely act. His waiting is not weakness, it is love giving time, but His judgment is certain. Let that move us to repent ourselves and to urge others to be reconciled to God through Christ while the door of mercy is still open.