The Fwer looks at the story of the jailer and goes away understanding that belief lead to salvation.
30 And he brought them out and said, “Sirs, what must I do to be saved?”
31 So they said, “Believe on the Lord Jesus Christ, and you will be saved, you and your household.” 32 Then they spoke the word of the Lord to him and to all who were in his house. 33 And he took them the same hour of the night and washed their stripes. And immediately he and all his family were baptized. 34 Now when he had brought them into his house, he set food before them; and he rejoiced, having believed in God with all his household.
The jailer is not being told that he is saved by believing, but will believe by being saved.
“and he rejoiced, having believed in God with all his household”.
I go away understanding that salvation results in belief!