No She was BETROTHED. For all intents and purposes they were WED.
If they were not married but only “engaged” it would not have been necessary for Joseph to divorce her.
Matthew 1:19 “Ἰωσὴφ δὲ ὁ ἀνὴρ αὐτῆς, δίκαιος ὢν καὶ μὴ θέλων αὐτὴν δειγματίσαι, ἐβουλήθη λάθρᾳ ἀπολῦσαι αὐτήν.”
Matthew 1:19 “Whereupon Joseph her husband, being a just man, and not willing publicly to expose her, was minded to put her away privately”. The word ἀπολῦσαι from Strong’s concordance 630 /apolýō ("to release") is specifically used of divorcing a marital partner
We see the exact same term used when Jesus is discussing marriage and divorce in Mt 1:19, 5:31,32, 19:7-9.
On the way to Bethlehem the Scripture still refers to them as BETROTHED.
Luke 2:5 “to be enrolled with Mary, his betrothed, who was with child.”
It was common practice that there was a period of “betrothal” (usually one year) and then the bridegroom took his betrothed as his wife and the marriage was consummated. This was done for several reasons but the one in question here was to ensure the bride was a virgin and not pregnant with another man’s child. The bill of divorce Joseph contemplated giving Mary was because she was found with child before they were come together. I thought you already knew this verga.