Most Christian churches I know have been trying to win non Christians to the Christian faith. Other ways we call it are sharing the faith , evangelizing etc . We even try to convert fellow Christians and our fellow Christians try to convert us. Convert may not be the best word to use but you may use your own if you like.
On one book I am reading about sharing the faith, the author mentioned that some or many people are waiting to be invited to go to church while some Christians are shy about sharing the faith.
But I believe time is short so those who are waiting to be invited and those who are shy about sharing their faith, I will encourage them/us to make their/our move. To pray that God will lead them/us to people who need or know the Lord Jesusand for us to use our time wisely because time is short.