Answer:
As a Catholic I can say that in a moment the salvation depended on the words of Our Lady when she accepted the will of the Lord by saying: "Behold, I am the handmaid of the Lord. May it be done to me according to your word."
We, as Catholic, believe that God created humans with freedom (free will) and that God respects human freedom. Jesus Christ is the greatest proof that God respects our freedom. Jesus is "the image of the invisible God" (Col 1:15), and therefore is the one to whom we turn when we want to discover how God relates to people. Jesus did not force people to follow him or to do what was right. He chose Apostles, but he only invited them to follow, and when Judas turned against him, Jesus did not force him to choose the right thing. He allowed Judas to say no. When Jesus invited the rich young man to follow him, and the rich young man turned away, Jesus did not force him to change his mind (Mk 10:17-22). When Jesus said, "I am the bread of life," and many of his disciples refused to believe him, Jesus did not force them to accept his word; he let them walk away (John 6:60-71). Therefore, Jesus, the image of the invisible God, teaches us that God respects human freedom.
Now, is it possible that, in the most important event in human history, God would disregard human freedom and simply make Mary the Mother of God's Son without her consent? We read in Luke 1 that the angel announced God's will to Mary. The angel waits until Mary says, "Behold, I am the handmaid of the Lord. May it be done to me according to your word." Only then does the angel leave. This indicates that Mary consented to God's will.
The only other possibility is that Mary did not consent. In that case, she became pregnant by a miracle to which she did not freely consent! This would mean that the Son of God became a human being in the womb of a woman who did not want to become his Mother! This would mean that God completely disregarded human freedom and human choice in the one event which would begin the process of our salvation. This is clearly an impossibility. To summarize, there are two possibilities: God either invited Mary to become the Mother of God's Son and accepted her consent, or God simply made Mary the Mother of God's Son without her consent. The first choice, it seems to me, is consonant with the Bible and with our understanding of God as given us through Jesus Christ. The second presents an image of God which is pagan in its implications (for pagans, the gods simply used human beings) and which contradicts Scripture and the nature of God.