The virgin birth is the ultimate impossibility. As a rule, conception never takes place apart from the physical union of two cells, which are provided by physically male and female humans. In the incarnation, God's Spirit conceived Christ in Mary's womb without the presence of a male cell.
Luke 1:34-37 Mary said to the angel, "How can this be, since I am a virgin?" The angel answered and said to her, "The Holy Spirit will come upon you, and the power of the Most High will overshadow you; and for that reason the holy Child shall be called the Son of God. . . . For nothing will be impossible with God."
Consider Mary's statement, "from this time on all generations will count me blessed." (Luke 1:48). These were the words of a young, unmarried pregnant woman, from a poor Galilean village, with no "proof" of her extravagant claim. Normally, such women might be called many things, none of which are remotely similar to "blessed." She would likely have been cast aside and forgotten by her contemporaries rather than remembered with joy and admiration by God-honoring people in every future generation.
Consider also that the angel called this baby a "holy child." Children conceived outside of wedlock have been given various unfortunate labels, but this One would be called the Son of God.
Leave it to God to bring His ultimate blessing and fulfillment of prophecy through such apparently ignominious circumstances! Leave it to God to draw such a history-breaking event out of common insignificance and obscurity! Leave it to God to unveil His purity to the world through the false appearance of immorality! Leave it to God to reveal His miraculous plan to humble, unnoticed servants rather than the religious elite in Jerusalem! Leave it to God to do such seemingly illogical things for His own glory!
He continues to use humble, obscure, overlooked, God-centered, love-motivated, grateful, trusting servants to fulfill His will in our day - as the way is prepared for the second advent of the Son of God.