It is certainly the role of the church to evangelize. When we talk about evangelizing, what we mean is declaring the good news. The good news is that Jesus Christ came to save sinners and we want to make that known as far and wide as possible. The church does that in all sorts of ways.
The gospel, the good news, should certainly be heard in worship services. The good news should be heard in various teaching ministries of the church. The good news should be heard in the lives and words of members of the church as they live and communicate with people. There can be special activities of the church in the interest of evangelism, but there are also the ordinary activities of the church and the ordinary lives of Christians as they live and speak that ought to testify to Christ and the newness of Christ.
Sometimes people get the idea that evangelism always requires saying, “You need to make a decision for Christ.” That often puts so much pressure on individual Christians that they get tongue-tied. I think evangelism very much occurs when we say what God has done for us. It is a testimony and an invitation to anyone hearing us that they can pursue and ask questions if they are interested. That’s a form of evangelism.
I don’t want to imply that there is no place for talking to people and challenging people, but there is also a place simply to testify what God has done for me and let that testimony challenge the lives, and experiences, and thought processes of other people. All that to say, an essential part of the life of the church is making the good news known.