Well, first of all it seems to me that we're implying God only (or mainly) works in our church services. If we place particular importance on our non-Christian friends coming to church on a Sunday, doesn't that mean we think there's something special about that Sunday meeting?
Stating it the other way, doesn't it imply that we think God is not really at work in our day-to-day lives, as we work, play and socialise? Surely he is! If we're a follower of Jesus then he's with us all the time and he wants to work through us all the time, right? So we should pray for and expect opportunities to show Godly love to our friends and neighbours, to talk with them about our faith, and to pray with them. We can share the good news of Jesus with them in the midst of daily life; it doesn't have to be the pastor, the evangelist or the music leader on a Sunday who does this.
I've been reading and loving the blog of a guy called Mike Breen, who used to lead a big church in Sheffield and is now involved in an organisation that, in their own words, aims to 'take 30 years of learning from a very post-Christian England context, as well as penetrating Biblical insights, and come alongside churches and organizations who are finding the North American mission field more post-Christian with each passing day'.
Breen tells the story of the Sheffield church, St Thomas', in this blog post. Check out this excerpt which explains how they focus on helping people become disciples, followers of Jesus Christ, instead of focusing on making the Sunday service as attractive as possible to non-Christians:
St Thomas Sheffield isn’t a massive church and the center of a movement because it’s got the best worship service. Or the best digital experience. Or the best preachers/teachers in the world. It’s because everything they do is about making disciples. They honestly believe if you make disciples and release them to lead, release them into their destiny, release them to be Agents of the Kingdom, everything will change.
If we are great at making the disciples, church growth will never be a problem because to be a disciple means you’re a missionary. It was never OK for us to be a large church and have very few missionary disciples. So we built something where that couldn’t happen. Making disciples was in the DNA from the very beginning and it has just carried through.
It's all about helping people become genuine followers of Jesus, people who hear the word of God and do it. The best Sunday church experience in the world will achieve very little if we're not making disciples and empowering each other to do the works of God's kingdom.