Physically, it is not possible. While certain organic species are able to procreate without cross-gender mating. Humans have never done so apart from the miraculous conception here. It is not possible to formulate any scientific explanation for the fertilization and pregnancy process described in this passage. Nor are we given any information on the nature of God’s role in this birth, other than attributing Mary’s pregnancy to divine intervention.
A further question developed in the history of the church concerning Mary’s perpetual virginity. The Roman Catholic Church adopted this teaching, which led to the near deification of Mary. We note that Mary had decided to marry before the announcement of her special birth (she was the “blessed virgin” surely, but also the “blessed financ’ee”), and that Matthew 1:25 clearly points to sexual union between Joseph and Mary after Jesus’ birth.
MATTHEW 1:25 – 25 And knew her not till she had brought forth her firstborn son: and he called his name Jesus.