Leithart Asks - on Justification and Baptism

Peter Leithart has a question that every child who has memorized the Westminster Shorter Catechism should be able to answer: "If baptism is not a public declaration of justification, where and when does that public declaration take place?" (link)

Westminster Shorter Catechism #38
Q: What benefits do believers receive from Christ at the resurrection?
A: At the resurrection, believers being raised up in glory,1 shall be openly acknowledged and acquitted in the day of judgment,2 and made perfectly blessed in the full enjoying of God,3 to all eternity.4

[1] 1 Corinthians 15:42-43. So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption: It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power.
[2] Matthew 25:33-34. And he shall set the sheep on his right hand, but the goats on the left. Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world.
Matthew 10:32. Whosoever therefore shall confess me before men, him will I confess also before my Father which is in heaven.
[3] Psalm 16:11. Thou wilt shew me the path of life: in thy presence is fulness of joy; at thy right hand there are pleasures for evermore.
1 Corinthians 2:9. But as it is written, Eye hath not seen, nor ear heard, neither have entered into the heart of man, the things which God hath prepared for them that love him.
[4] 1 Thessalonians 4:17. Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. [See preceding context.]

As Matthew Henry puts it:

4. Shall they be openly acknowledged in the day of judgment? Yes: Him will I confess before my Father which is in heaven, Matt. 10:32. Will God own them as his own? Yes: They shall be mine, saith the Lord, in that day when I make up my jewels, Mal. 3:17. And will that be their honour? Yes: If any man serve me, him will my Father honour, John 12:26. Shall they be openly acquitted? Yes: for their sins shall be blotted out when the times of refreshing come, Acts 3:19.

Westminster Larger Catechism

Q. 90. What shall be done to the righteous at the day of judgment?

A. At the day of judgment, the righteous, being caught up to Christ in the clouds,[389] shall be set on his right hand, and there openly acknowledged and acquitted,[390] shall join with him in the judging of reprobate angels and men,[391] and shall be received into heaven,[392] where they shall be fully and forever freed from all sin and misery;[393] filled with inconceivable joys,[394] made perfectly holy and happy both in body and soul, in the company of innumerable saints and holy angels,[395] but especially in the immediate vision and fruition of God the Father, of our Lord Jesus Christ, and of the Holy Spirit, to all eternity.[396] And this is the perfect and full communion, which the members of the invisible church shall enjoy with Christ in glory, at the resurrection and day of judgment.

[390] Matthew 25:33. And he shall set the sheep on his right hand, but the goats on the left. Matthew 10:32. Whosoever therefore shall confess me before men, him will I confess also before my Father which is in heaven.

[391] 1 Corinthians 6:2-3. Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters? Know ye not that we shall judge angels? how much more things that pertain to this life?

[392] Matthew 25:34, 46. Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world.... And these shall go away into everlasting punishment: but the righteous into life eternal.

[393] Ephesians 5:27. That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish. Revelation 14:13. And I heard a voice from heaven saying unto me, Write, Blessed are the dead which die in the Lord from henceforth: Yea, saith the Spirit, that they may rest from their labours; and their works do follow them.

[394] Psalm 16:11. Thou wilt show me the path of life: in thy presence is fulness of joy; at thy right hand there are pleasures for evermore.

[395] Hebrews 12:22-23. But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect.

[396] 1 John 3:2. Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is. 1 Corinthians 13:12. For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known. 1 Thessalonians 4:17-18. Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. Wherefore comfort one another with these words.