Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, "Men and brethren, what shall we do?" Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call." And with many other words he testified and exhorted them, saying, "Be saved from this perverse generation."
Acts 2:37-40

When the believers in the crowd asked Peter “what shall we do?” his reply was “repent…and be baptized.” He did not mention believe. Why not, if believing is the means by which we receive saving grace based on the person and work of Christ? The simple answer is found in verse thirty-seven.

They had “heard” the gospel preached. They were “cut to the heart.” They asked what they were to “do.”

They had “heard” the gospel preached. The gospel is the power of God to salvation. It is the power to convert and cause a person to “believe” with or without a specific instruction to believe. These people hard the gospel and believed.

They were “cut to the heart.” The power of God to salvation cuts people to the heart. They are convicted of their sin and convinced that Jesus is the only means of salvation. That these people were “cut to the heart” means they were both convicted and convinced.

They asked what they were to “do.” Having heard the gospel, these people believed, and were “cut to the heart,” as evidenced by the fact that they asked, “what shall we do?”

These three are evidence that they did believe.

We must look for biblical evidence of salvation (as was evident in these people), not for insisting in formulas that may or may not lead to or give evidence of true conversion.