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Noah is an interesting example as I would argue he was perfect in his use of the Law, that is he used the atonement as understood and designed for Israel.

That sounds problematic. First, the scripture simply says "Noe was a just and perfect man in his generations, he walked with God" (D-R Gen 6:9). The focus is on how he "walked" even before any law was given to him, let alone to Israel. More fundamentally, we Catholics do not believe there are two atonements, one for Israel and another for Christians. We believe that the work of Christ on the Cross atoned for all sin, including, retroactively, sins of the Jews and Gentiles prior to Christ. The historical role of Israel was to receive special law much like a beloved child receives extra schooling, in order to prepare the human race for the Redeemer, Who alone atones for anyone, Jew or Gentile, who would "walk" with Him. That schooling was not salvific in itself. It was, simply put, there to produce Mary the ever Virgin, who would be a fit mother for the Incarnate God.

Which leads to your question, "how Christ prevented Mary from sinning after his birth?"

Here we are looking at a situation where eternal, preexisting Christ designed His own mother, much like the Father designed His own people of Israel. Somehow that preparation, through the judges, kings apnd prophets of Israel, resulted in a human perfection that worked her way back to the purity of design which was Eve before the Fall. How did the Father make Eve? The answer is, perfect. Mary is second Eve, -- through her the second creation took place. Do you know that baptism, your second birth, makes you perfect? How? I don't know. It is a Holy Mystery, -- a Sacrament of the Church. The perfection of Mary at her conception was akin to that.

3 Know you not that all we, who are baptized in Christ Jesus, are baptized in his death? 4 For we are buried together with him by baptism into death; that as Christ is risen from the dead by the glory of the Father, so we also may walk in newness of life. 5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection.
(Romans 6)

St. Justin Martin reasoned:

Chapter 100. In what sense Christ is [called] Jacob, and Israel, and Son of Man
Justin: Then what follows—'But You, the praise of Israel, inhabitest the holy place'—declared that He is to do something worthy of praise and wonderment, being about to rise again from the dead on the third day after the crucifixion; and this He has obtained from the Father. For I have showed already that Christ is called both Jacob and Israel; and I have proved that it is not in the blessing of Joseph and Judah alone that what relates to Him was proclaimed mysteriously, but also in the Gospel it is written that He said: 'All things are delivered unto me by My Father.' and, 'No man knows the Father but the Son; nor the Son but the Father, and they to whom the Son will reveal Him.' Matthew 11:27 Accordingly He revealed to us all that we have perceived by His grace out of the Scriptures, so that we know Him to be the first-begotten of God, and to be before all creatures; likewise to be the Son of the patriarchs, since He assumed flesh by the Virgin of their family, and submitted to become a man without comeliness, dishonoured, and subject to suffering. Hence, also, among His words He said, when He was discoursing about His future sufferings: 'The Son of man must suffer many things, and be rejected by the Pharisees and Scribes, and be crucified, and on the third day rise again.' Matthew 16:21 He said then that He was the Son of man, either because of His birth by the Virgin, who was, as I said, of the family of David and Jacob, and Isaac, and Abraham; or because Adam was the father both of Himself and of those who have been first enumerated from whom Mary derives her descent. For we know that the fathers of women are the fathers likewise of those children whom their daughters bear. For [Christ] called one of His disciples—previously known by the name of Simon—Peter; since he recognised Him to be Christ the Son of God, by the revelation of His Father: and since we find it recorded in the memoirs of His apostles that He is the Son of God, and since we call Him the Son, we have understood that He proceeded before all creatures from the Father by His power and will (for He is addressed in the writings of the prophets in one way or another as Wisdom, and the Day, and the East, and a Sword, and a Stone, and a Rod, and Jacob, and Israel); and that He became man by the Virgin, in order that the disobedience which proceeded from the serpent might receive its destruction in the same manner in which it derived its origin. For Eve, who was a virgin and undefiled, having conceived the word of the serpent, brought forth disobedience and death. But the Virgin Mary received faith and joy, when the angel Gabriel announced the good tidings to her that the Spirit of the Lord would come upon her, and the power of the Highest would overshadow her: wherefore also the Holy Thing begotten of her is the Son of God; and she replied, 'Be it unto me according to your word.' Luke 1:38 And by her has He been born, to whom we have proved so many Scriptures refer, and by whom God destroys both the serpent and those angels and men who are like him; but works deliverance from death to those who repent of their wickedness and believe upon Him.
Dialogue with Trypho (Chapters 89-108)

Mary simply would not sin. God can do that in a man, -- or woman. She is by conception what we are to become by the work of Christ in us gradually. This is how the Apostles describe sanctification:

2 Grace to you and peace be accomplished in the knowledge of God and of Christ Jesus our Lord: 3 As all things of his divine power which appertain to life and godliness, are given us, through the knowledge of him who hath called us by his own proper glory and virtue. 4 By whom he hath given us most great and precious promises: that by these you may be made partakers of the divine nature: flying the corruption of that concupiscence which is in the world. 5 And you, employing all care, minister in your faith, virtue; and in virtue, knowledge; 6 And in knowledge, abstinence; and in abstinence, patience; and in patience, godliness; 7 And in godliness, love of brotherhood; and in love of brotherhood, charity. 8 For if these things be with you and abound, they will make you to be neither empty nor unfruitful in the knowledge of our Lord Jesus Christ. 9 For he that hath not these things with him, is blind, and groping, having forgotten that he was purged from his old sins. 10 Wherefore, brethren, labour the more, that by good works you may make sure your calling and election. For doing these things, you shall not sin at any time.
(2 Peter)

and

12 ...with fear and trembling work out your salvation. 13 For it is God who worketh in you, both to will and to accomplish, according to his good will. 14 And do ye all things without murmurings and hesitations; 15 That you may be blameless, and sincere children of God, without reproof, in the midst of a crooked and perverse generation; among whom you shine as lights in the world
(Philippians 2)

What a saint works out with fear and trembling step by step, for it is God working in him, Mary had all at once, for it was God working in her.