Every person has a conscience. This is a God-given alarm bell that activates when we do something against it. If I look at a woman in a short skirt on a windy day with lust, my conscience will tell me, "That is not right! You are committing adultery in your heart!" If I am to obey my conscience then I will ask forgiveness from the Lord and strength from the Holy Spirit to keep my mind and heart clean.
When a person is convicted in their conscience, they respond in two different ways. They try to discredit what it is saying to them either through an action, or someone else reminding them that they are doing wrong, to ease their conscience. That is why there are so many acidic and abusive reactionary posts on this forum - it is because their conscience has been pricked and they don't want to obey it, and so they rubbish the person who posted the comment that has pricked it.
Or, if a person allows their own conscience to teach them right from wrong, when they hear something that activates their conscience, they will listen further and want to know more about how to ease their conscience in the right way. When Nathan challenged David about his adultery, David listened to his conscience and got right with God. But when King Ahab heard the prophecy of Michaiah and his conscience was pricked, he threw the prophet into prison and listened to his own false prophets to ease his conscience.
The mistake that many Christian workers make is to try and speak to the unsaved person's mind instead of their conscience. Asking what "god" they worship does not get to their conscience. But getting them to examine their conduct through the Ten Commandments will; because our conscience is inseparately linked to the Ten Commandments.
Those who protest that "we are not under the law", and "preaching law is just condemning people and not attracting them to Christ", are missing the Biblical statement that those who are without Christ are condemned already. Getting them to test their conduct in terms of the Ten Commandments is just reminding their consciences that they are condemned because they are not keeping the Commandments and therefore are in danger of the judgment.
This is why the majority of Christian workers are just wasting their time and effort trying to get the gospel across to the unsaved, because they are not succeeding, and often they become discouraged over the lack of results and just give up and concentrate on their church attendance and religious activities.
Sorry but I like the subtle approach and not the confrontational one that you are advocating as it does work, but it requires more time as the refurbished Salvation Gospel Covenant is introduced to them. That is the treasure that the householder is expected to bring out for others to see.