Not at the time of the conception and not at the time Joseph was wondering if he should put her away quietly.
They were betrothed.
A woman does not become a mother until she gives birth. At the time of Jesus' birth, Joseph and Mary were married.
While it's true that the story of her virgin impregnation (Immaculate Conception) is a core belief of the Christian faith, and is one of the means by which Christians assert the divinity of Jesus (Luke 1:24-37), the biblical author made sure to point out that Mary was married when Jesus was born.