After I lead people to Christ, should I offer them immediate assurance?
It isn’t your task as an evangelist to give immediate assurance to people you lead to Christ. The Holy Spirit will do that work: “The Spirit Himself bears witness with our spirit that we are children of God” (Romans 8:16).
There are, however, many promises in Scripture you can share that the Holy Spirit will use to help your newly converted friends gain assurance of their eternal destiny (e.g. John 3:161 John 5:1). Those promises of the gospel offer what is called “objective assurance” to genuine believers. Even a brand-new believer can look to such promises and find a measure of assurance–the thief on the cross gained it when the Lord promised Him a place in paradise.
There are other passages in Scripture that speak of subjective assurance. For example, 1 John 2:3 says, “By this we know that we have come to know Him, if we keep His commandments.” That assurance will grow and deepen as person walks consistently with the Lord. Should a Christian persist in sin for a time, he will forfeit that aspect of assurance for as long as he grieves the Holy Spirit.
Both the objective and subjective means of assurance are spoken of in Romans 15:4: “Whatever was written in earlier times was written for our instruction, that through perseverance [subjective] and the encouragement of the Scriptures [objective] we might have hope.” That process is part of the Christian’s lifelong spiritual growth.
There’s really nothing to gain by giving new converts immediate assurance of salvation. They will realize true assurance through the promises in Scripture and by sensing the Spirit’s work–the Holy Spirit will bear witness with their spirit that they are children of God. No formulas can bring about such assurance.