Now those who were scattered after the persecution that arose over Stephen traveled as far as Phoenicia, Cyprus, and Antioch, preaching the word to no one but the Jews only. But some of them were men from Cyprus and Cyrene, who, when they had come to Antioch, spoke to the Hellenists, preaching the Lord Jesus. And the hand of the Lord was with them, and a great number believed and turned to the Lord. Acts 11:19-21

God uses what opposes Him. Sound doctrine, for example, has often been hammered out because false doctrine needs to be corrected. In a similar fashion, persecution has often been used by God to expand the Church.

You will remember that Jesus issued the Great Commission (Matthew 28:18-20 & Acts 1:8), in which He commanded His disciples (including us!) to take the gospel here, there, and everywhere. Instead, for the most part the believers remained huddled in Jerusalem. Persecution arose and stirred the believers to scatter, and as a result, the gospel went to more people in more places.
Lesson Number One: we ought not wait for persecution (or any adversity) to obey the Great Commission. We cannot all “Go to the ends of the earth,” but we can speak of Jesus where we live, and support those who do “Go” with finances and with prayer.

The first ones to venture out preaching the gospel limited their audience to other Jewish people. It is what happened, but it was a mistake.
Lesson Number Two: We must not choose who we speak with about Christ. It is not up to us to determine who God may or may not be pleased to save. Let us speak to and pray for all we encounter.

The results was that “a great number believed.”
Lesson Number Three: God saves His people, but He has sovereignly chosen to do so through those He has already saved, as they speak to and pray for non-believers, whoever and wherever they are.