I recently reach the book ANY 3 which is about evangelism among Muslims. His premise is that we should lead with the gospel. While people often first build a friendship, the author argues for giving the gospel right up front with every opportunity that comes your way. It is aggressive. It is based on the fact that it is the power of the gospel that changes lives. It is not our relationships, our apolgetics or our good deeds. The gospel is what changes lives so why not give it.
You never know when someone will be ready to listen. We often try to second guess who might be interested and open but you never know who will respond in a positive way. Like a good fisherman, you should just keep casting. If you do that enough, you will eventually catch a fish.