There would have been thousands of women in Nazareth and in the whole of Israel; and out of these women, God chose our Blessed Virgin Mary to be the mother of Christ. But why God Almighty did chose Mary to be the mother of Christ, out of the many women in the whole of Israel and indeed the world; we would have to be God Himself to be able to answer that question because it is God's mind that we are trying to understand. However we get to have a glimpse of God's mind in Bible, where He has revealed many of His secrets to us.
As per God’s plan of salvation:
When we look at God to be All-knowing and Almighty, we have a view of what was happening in God's scheme of salvation.
1 Peter 1:20 He was foreknown before the foundation of the world but was manifested in these last times for your sake.
Here Bible tells us that God planned the salvation of mankind well before the foundation of the world. In that case God must have planned well in advance, every milestone of that plan of salvation.
God planned that Christ would be born into the world by a woman; the same way that all human beings were born. He is God and it is very possible to send Christ into the world without the process of being born by a woman, but that was not God's plan and He had revealed this plan through the prophets in the scriptures.
Possible reason why Mary was chosen:
God prefers humble and lowly: Throughout the Bible we find that there is a general theological and narrative of God's preferential option for the least, the last, and the lost. In Genesis, the stories of Abraham (a wandering nomad...a nobody), Isaac (the second born of Abraham), Jacob (the second born of Isaac), and Joseph (11th of Jacob's sons) reveal a pattern that would have been quite unusual: it was usually the eldest son who received the primary portion of the inheritance, but in these stories the "least" become the greatest. The Old Testament presents a preferential option for the least.
So God chooses to work through one of the lowliest people imaginable...an unmarried peasant girl from a little off-the-map town in a province that the most powerful empire in the world looked on with great scorn. To further underscore this theme, Jesus was born in a stable and was countenanced by shepherds and foreigners. All these events help us to have the glimpse of God's mind and the possible reason why He chose Mary to bear Jesus.
God is Holy: God himself is holy, and it would only require a holy vessel to give birth to Christ and that holy vessel must be a virgin; but the question may arise out of the whole of Israel: was Mary the only virgin?, The answer would be a no but Mary was chosen not only because of her virginity but because she possessed the purest of hearts, and that was the essential ingredient that God needed from her to be the mother of Christ. A pure heart as at then required constant prayers directly to God from the heart and Mary was the only virgin in Israel and indeed the world to possess the purest of hearts and be a virgin.
Foreseeing all these qualities, Mary was ordained for her role, even prior to her own birth. God decided that he would choose her even before she was born. That is why she is Immaculate Conception. It was all God's plan that was taking shape. God made Mary free of original sin at the time of her own conception in readiness for her role as Christ’s mother.
To quote the Vatican II document Lumen Gentium:
“the holy Fathers see [Mary] as used by God not merely in a passive way, but as freely cooperating in the work of human salvation through faith and obedience.”
So Mary was free to reject this role. Yet Mary grew up perfectly as God planned. Mary was a simple young woman of no great talent. She was not rich or famous. However, she did develop the qualities that God was looking for to bear his Son: Courage, willingness, love for God, and purity. Mary was a brave woman who would not shrink from this monumental task. That is how she bravely said:
Luke 1:38 So Mary said, “Yes, I am a servant of the Lord; let this happen to me according to your word.” Then the angel departed from her.
She was an incredible role model then and now. Mary exhibited complete femininity in her response to the angel Gabriel. She surrendered completely to the will of God. She had much to lose potentially - her husband, reputation, and even her life - yet she trusted in the providence of God. She was knowledgeable about her own religion and surrendered freely to the will of God. Mary understood the Jewish prophecies foretelling the Messiah.
We could add another reason that God chose Mary to be the mother of Christ; the reason is that God still remains God himself and just like when he created man in Genesis, he holds the reason for the mystery and why it has to be so.