Old Testament Israel and missions

Why did the Israelites do little to spread God's Word (at that time, the promise of the Savior) to other nations?

I am not sure what led you to that conclusion, but it is not an accurate one. Certainly, the ceremonial laws that God gave to the people of Israel were designed to keep them separate from the heathen nations around them, but God’s will was that his people share the news of a promised Messiah with others. And they did.

I can recommend to you two resources that elaborate more on that truth. This first link will take you to a “Light for our Path” column that addressed a question that was similar to yours: “Were the Jews to spread the message about the promised Savior even to Gentiles, as we do mission work today?”

This second link will give you access to a short paper: “The Mission Mindset of God’s Old Testament People.”

God had promised Abraham: “All peoples on earth will be blessed through you” (Genesis 12:3). The people of the world would be blessed through the Savior who would come through Abraham’s lineage. The people of the world needed to hear of that promised Savior, the Messiah. God’s Old Testament people of Israel spread the word.