To answer this, we need to look at the theological basis of marriage in Christianity first, and Middle-to-Late Antiquity culture in the Greco-Roman Mediterranean, which essentially meant Christian world all the way until the 10th century or so, second.

When Jesus appeared, he was only one of the many ''radical'' Jewish preachers at the time, who was preaching his own brand of Judaism, which has, to some people, become corrupted and strayed away from God. It just so happened that this particular movement survived, grew massively in size and left some records from the early days, so we know about it.

We can be fairly certain what he and the Apostles thought on marriage. I don't have the English translation with me atm, so if you want to verify my claims I'll be more than happy to provide you with relevant verses later, but in essence, Christian view of marriage in the early days was that it has always been monogamous in theory, but that God allowed it to happen for variety of reasons. If you want, it's kinda like marijuana in today's United States: illegal, but federal government basically allows it.

Christ and Apostles were, from their point of view, not radicals, but people who were only preaching what was already in the Mosaic Law.

That was, in essence, theological basis for Christian view of marriage. Now, let's deal with the cultures Christianity had to work with on its way to world domination.

Even though Christianity originated in the Roman province of Judea, during the first decades and centuries after the Crucifixion it's main 'area of operations' was in the Hellenized/Hellenic parts of the Eastern Mediterranean, predominantly in cities. Notable exception is Rome. We know that by simply reading the names of the cities to which Paul gave his famous Epistles: Thessaloniki, Galatia, Ephesus, Philippi, Corinth, etc. And later, of the five cities of Church Pentarchy (Rome, Constantinople, Jerusalem, Antioch and Alexandria), three of them were Greek speaking, with Jerusalem being under heavy Greek cultural influence.

Greek culture, as well as Roman culture, already had a concept of marriage as an institution which is in its nature monogamous, so preachers didn't have to completely reinvent the concept of marriage for the unbelievers, as they maybe would if they were preaching in today's Saudi Arabia or Somalia.

So, where were the difficulties? The answer lies in the other aspects of Greco-Roman sexual culture, such as institutions of concubinage, relatively easy divorce, infidelity, ''homosexuality'' (quotation marks mine, because what we think of when we hear that word has little resemblance to same-sex relations thousands of years ago), prostitution, etc.

During the dying days of the Republic, Mark Antony made a great scandal when he married Cleopatra when he was still married to Octavians' sister, Octavia. It was surely astroturfed by Octavian to turn people against Antony, but it is telling that nobody objected when Rome essentially said ''Yeah, legally this didn't happen''. Even before the marriage, Romans were more concerned that an Eastern viper has corrupted a good Roman than with the fact that he already had a wife back home.

It took a great amount of time and trouble to get rid of the most aforementioned institutions, and why it happened is up to debate, but the simplest answer is that all of those institutions were in their nature religious, as almost everything was back then, so as Christianity progressed and gained influence, these things weakened gradually even with non-Christians. For more extensive answer regarding Greek understanding, I think u/Cleopatra_Philopater wrote a very thorough explanation which I can't link right now.

And why have the Jews essentially abandoned polygamy? Technically, they haven't. It is still allowed for Orthodox Jews to marry multiple women, which sometimes can create a complete chaos in religious communities. But, essentially nobody does it anymore and the reason for that is that the Jews were dispersed after their Great Revolt and they have more or less assimilated, at least in that regard, to the numerically superior culture of their monogamous neighbours.