The ban on polygamy came in the New Testament with the words of Jesus in Matthew 19:6. Up until that time, due to the hardness of the people’s hearts, God did not impose that burden upon them. However, by the time of Jesus, the people were ready to receive such a “burden” (which is not really a burden since all of the laws of Jesus are light by the power of the Spirit). Jesus restored marriage in Matthew 19:6 to its original design. In the beginning marriage was between one man and one woman but over time, due to the hardness of the people’s heart, the people went astray from this practice and had multiple wives. God did not immediately forbid it because they weren’t ready for such a change until the time of Jesus, just like he didn’t immediately forbid slavery.
Think of it like this. My two year old daughter often tells me “no!” when I ask her to clean up her mess and I usually have to repeat myself several times followed by several other no’s until I give her a spanking. However, when my daughter turns 14 years old or so, I will expect her do it the first time I ask. The reason is because by then she will be mature enough to do something the first time I ask, whereas at her current age she just isn’t ready for that. This is the same way God deals with His people during salvation history. There were many things the people of God did in the Old Testament that God didn’t explicitly forbid since they were not mature enough to handle it. By the time Jesus, the people of God had matured enough in the faith to be ready to receive the fullness of the law, the law of Christ.