"Now Naaman was the commander of the army of the king of Aram…" 2 Kings 5:1
Naaman was an army commander of a foreign nation. He had fought successful battles against Israel. He worshipped in the temple of Rimmon. In every way you could think of, he was an outsider. He didn't belong in Israel. He had no claims on the God of Israel. He was locked into heathenism.
In one way he is like every one of us. Locked in sin, no desire for God, doing our own thing, not deserving a single thing from God except judgment. We have all been there. Then Jesus reached down in love and drew us into His family - He redeemed us and restored us to fellowship with our true Father.
What was it that turned our eyes toward Jesus? For many people, like Naaman, it was a problem or difficulty that they couldn't solve, that was dragging them down. They became desperate for a solution, even when suggested by a little girl. They would try anything…
Once we have been Christians for awhile we sometimes develop the same attitude that the Jews of Jesus' day had: You have to come join us before God will do anything for you. They actually got mad at Jesus when He pointed out cases where God had blessed non-Jews [Luke 4:25-28].
Yes, the greatest need people have is to know Jesus as Lord and Saviour, but that is not usually their greatest perceived need. We need to be careful that we are not using "spiritual blackmail" - i.e. If you come to Jesus He will solve your problem.
This is wrong on, at least, two levels. First, Jesus doesn't solve all our problems. Sometimes we come to Jesus and from a physical viewpoint things get worse! Just ask the 100,000 or so martyrs every year or those who are shunned by family, friends and employers for the Christian beliefs. So that is false advertising. Jesus will walk with us through our problems and pain and we can know the peace and joy of God throughout it, but they don't always go away. Sometimes, but not always.
Second, as we see with Naaman, God is willing to help and bless people outside the family. He doesn't try to force them into His circle in order to help them. You can pray for non-Christians to have healing, to have solutions to challenges, to get jobs, etc. without trying to "convert" them first or make them fell guilty after. Jesus hears your prayers. He cares about them. He went looking for the lost sheep.
If the blessings of Jesus do not eventually lead a person to come to Jesus as Lord and Saviour then the benefits are short term - one lifetime. Only those who know Jesus as Lord as Saviour have peace with God which is essential to true peace in life and a successful eternity, but we don't have to make that a condition for God to work in temporal ways in a person's life.