So impregnating a 16 year old girl would not be a problem.
And if there is no God, then CHRISTmas is rather silly.
More attractive an explanation is to posit a bit of pre-nuptial nookie on the part of Joseph.
Matthew, in his Gospel, is having none of that.
This was how the birth of Jesus Christ took place. His mother Mary was engaged to Joseph, but before they were married, she found out that she was going to have a baby by the Holy Spirit. Joseph was a man who always did what was right, but he did not want to disgrace Mary publicly; so he made plans to break the engagement privately.
While he was thinking about this, an angel of the Lord appeared to him in a dream ...
... and said, “Joseph, descendant of David, do not be afraid to take Mary to be your wife. For it is by the Holy Spirit that she has conceived. She will have a son, and you will name him Jesus - because he will save his people from their sins.”
To "do what is right" by the standards of the day, Joseph should have turned Mary out on the street and publicly denounced her infidelity. As "one of the good guys", he decided to break ranks with convention and, possibly, leave her private, unmarried but unthreatened, in her family's home.
Jesus (Yeshua, Joshua) means "God Saves" so the longer term message of CHRISTmas is reinforced by both Gospel writers.