The church service is designed for the believer and for the covenant community to meet with God. The best way to talk about the worship service is to recognize that it is a meeting between God and His people. Therefore, it is a place where God speaks to His people and His people speak to Him. God speaks to His people in the reading of the Word and the preaching of the Word, and we speak to Him in prayer, song, and confession. There is a back and forth between God and His people.
In 1 Corinthians 14, Paul talks about how unbelievers sometimes come into a worship service, and the experience of seeing God’s people speaking to Him and God speaking to them might cause an unbeliever to realize what he is missing in terms of knowing God and hearing God. It might even lead to conversion.
It is fine to have special gatherings and meetings for evangelism, but that’s not what a worship service is primarily about.