God prepares Mary & the Ark of the Covenant as a carrier of His presence freed from contagion

Romans 3:23  says, "All have sinned and fallen short of the glory of God." Further, 1 John 1:8 adds, "If any man says he has no sin he is a liar and the truth is not in him."

If this is the set of circumstances "How could anyone deem Mary was freed from contagion of all sin?

Not only that, Mary herself said, ‘My soul rejoices in God my Savior’ in (Luke 1:47). Does it suffice that she recognizes herself to be a sinner in admission that she needs a Savior?

Yes, Mary was "saved." Indeed, Mary needed a Savior. However, Mary was "saved" from sin in a most awe-inspiring manner. She received the grace to be "saved" completely from sin to avoid commission even the slightest transgression. If you believe that God has immeasurable power, do you think it’s impossible? 

Falling into a sin could be equated to a woman approaching unaware to a deep trench. Once falling into it, he needs someone to lower a rope and be saved. However, if someone were to caution her of the hazard ahead, she would be saved from falling caused by the warning. Similarly, Mary was saved from sin by obtaining the grace to be safeguarded from it. Nevertheless, she was still saved.

Both Romans 3:23 and 1 John 1:9 address personal sin rather than original sin. Romans 5  deals with original sin. And there are two exceptions to that general biblical model as well. 1 John 1:8  evidently refers to personal sin because in the next verse, John says, "If we confess our sins, he is faithful and just to forgive us our sins . . ." Personal sin is confessed than original sin.

The context of Romans 3:23 clarifies that it also points to personal sin: 

As it is written: "There is no one just, not one, there is no one who understands, there is no one who seeks God. All have gone astray; all alike are worthless; there is not one who does good, (there is not) even one. Their throats are open graves; they deceive with their tongues; the venom of asps is on their lips; their mouths are full of bitter cursing (Romans 3:10-14). 

Original sin is not something humans committed; it is something that’s inherited. Romans 3 deals with personal sin as it talks about commission of sin by the sinner. To sin, a person has to be aware of the act he/she is about to perform is sinful while liberally employing her/his will in doing it. The absence of proper faculties to enable to sin like mental disorder for example, children before the age of accountability and anyone who does not have the use of intellect and will cannot sin, which implies of exceptions to Romans 3:23.

So how do we know that Mary is an exception to the model of "all have sinned?"

The Scripture says, "And coming to her, he said, "Hail, favored one! The Lord is with you." But she was greatly troubled at what was said and pondered what sort of greeting this might be. Then the angel said to her, "Do not be afraid, Mary, for you have found favor with God." (Luke 1:28:30)

The angel did more than simply greet Mary, communicating a new name or title to her.  Generally speaking, when one greeted another with a name or title would be found in the immediate context. For example, "Hail, king of the Jews" inJohn 19:3  and "Claudias Lysias, to his Excellency the governor Felix, greeting" (Acts 23:26  are two examples of this; the reality that the angel substitutes Mary’s name in the greeting with "Favoured One" was something but common. Names and name changes in Hebrew culture.  Say,  Abram to Abraham  in Genesis 17:5, Sarai to Sarah, in Genesis 17:5   and Jacob to Israel in Genesis 32:28.

Notably, the names reveal something permanent about the one named. Abraham and Sarah transition from being a "father" and "princess" of one family to being "father" and "princess" or "mother" of the entire people of God (Romans 4:1-18 ; Isaiah 51:1-2). They become patriarch and matriarch of God’s people forever. Jacob/Israel becomes the patriarch whose name, "he who prevails with God," continues forever in the Church, which is called "the Israel of God" (Galatians 6:16). The People of God will forever "prevail with God" in the image of the patriarch Jacob.

St. Luke uses the perfect passive participle, she who has been favored, as his "name" for Mary. This verbal adjective, "favored," is not just expressing a simple past action. Greek has a different tense for this. The perfect tense is used to point out that an action has been completed in the past resulting in a present state of being. "Favored one" is Mary’s name. The average Christian is not completed in grace and in a permanent sense (Philippians 3:8-12). But according to the angel, Mary is favored/full of grace. Men sin, not because of grace, but because of a lack of grace, or a lack of collaboration with grace, in her/his lives. This greeting of the angel implies of the unique character and calling of the Mother of God. Only Mary is given the name "favored one" and in the perfect tense, pointing out that this permanent state of Mary was completed. 

The Ark of the Covenant contained three "types" of Jesus inside: manna, Aaron’s rod, and the Ten Commandments. Comparatively, Mary bore the fulfilment of all these types in her body. Jesus is the "true manna from heaven" (John 6:32), the true "High Priest" (Hebrew 3:1), and "the word made flesh" (John 1:14).

The glory cloud was representative of the Holy Spirit, and it "overshadowed" the Ark when Moses consecrated it in Exodus 40:32-33. Put side by side with: And the angel said to her in reply, "The holy Spirit will come upon you, and the power of the Most High will overshadow you. Therefore the child to be born will be called holy, the Son of God. (Luke 1:35) .

David "leaped and danced" before the Ark when it was being carried into Jerusalem in procession in 2 Samuel 6:14-16. Put side by side with: As soon as Elizabeth heard the sound of Mary’s salutation, John the Baptist "leaped for joy" in her womb (Luke 1:41-11).

The Ark of the Lord "stayed in the house of Obededom . . . three months" in 2 Samuel 6:11. Put it side by side with: " Mary remained with her (Elizabeth) about three months and then returned to her home" (Luke 1:56). 

"Adam" and "Eve" are revealed simply as "the man" and "the woman" before the woman’s name was changed to "Eve" (mother of the living") after the fall (Genesis 2:21). Looking at the New Covenant, Jesus is explicitly referred to as the "last Adam," or the "New Adam" in 1 Corinthian 15:45. And Jesus Himself points out that Mary is the prophetic "woman" or "New Eve" of Genesis 3:15  when He refers to His mother as "woman" in John 2:4 and 19:26. Further, St. John refers to Mary as "woman" eight times in Revelation 12. As the first Eve brought death to all of her children through breaking the laws and listening to the words of the ancient serpent, the devil, the "New Eve" of Revelation 12 brings life and salvation to all of her children through submission. The same "serpent" who tricked the original woman of Genesis is revealed, in Revelation 12, to fail in his attempt to prevail over this new woman. The New Eve triumphs over the serpent and as a result, " Then the dragon became angry with the woman and went off to wage war against the rest of her offspring, those who keep God's commandments and bear witness to Jesus. It took its position on the sand of the sea" (Revelation 12:7).

In conclusion, if Mary is the New Eve and New Testament completions are always more glorious than their Old Testament precursors, it would therefore be improbable for Mary to be conceived in sin.

Reference:  

Tim Staples, Hail Mary, Conceived Without Sin, http://www.catholic.com/magazine/articles/hail-mary-conceived-without-sin