That is not how Jewish custom regarding betrothal work. One you were bethrothed the ONLY way the marriage would not occur would be because one of the two were unfaithful. Which of course is why we see Joseph considering this very thing but his intention was to do it quietly.
Matthew 1: 8 Now the birth of Jesus [r]Christ was as follows: when His mother Mary had been betrothed to Joseph, before they came together she was found to be with child by the Holy Spirit. 19 And Joseph her husband, being a righteous man and not wanting to disgrace her, planned [t]to send her away secretly. 20 But when he had considered this, behold, an angel of the Lord appeared to him in a dream, saying, “Joseph, son of David, do not be afraid to take Mary as your wife; for the Child who has been [v]conceived in her is of the Holy Spirit. 21 She will bear a Son; and you shall call His name Jesus, for [w]He will save His people from their sins.” 22 Now all this [x]took place to fulfill what was spoken by the Lord through the prophet: 23 “Behold, the virgin shall be with child and shall bear a Son, and they shall call His name [y]Immanuel,” which translated means, “God with us.” 24 And Joseph [z]awoke from his sleep and did as the angel of the Lord commanded him, and took Mary as his wife, 25 [aa]but kept her a virgin until she gave birth to a Son; and he called His name Jesus.
#1 scripture calls Joseph Mary's HUSBAND
#2 scripture plainly states that he kept her a virgin UNTIL she gave birth...
Without consummating the marriage a man and woman are NOT husband and wife.
The idea that Mary didn't marry Joseph is false. The idea that Mary was a virgin the rest of her life is a lie. The idea that Mary and Joseph is untrue given that A) she did marry Joseph, B) if they did not have sex the marriage is not consummated and C) unless Mary was barren she HAD other children because birth control did not exist