John, infants cannot intellectually understand the gospel before they die as infants. Adults cannot hear the gospel being preached when they are asleep. The jailer was asleep when Paul and Silas were singing praise hymns. The sequence of events is clear:
1. Paul and Silas sang while the other prisoners listened at midnight.
2. An earthquake occurred.
3. The jailer was roused out of his sleep.
4. The jailer assumed the prisoners had escaped.
5. The jailer was about to kill himself.
6. Paul let the jailer know that all the prisoners were still there.
7. The jailer asked, "What must I do to be saved?"
8. Paul and Silas answered his question.
9. Paul and Silas "spoke the word of the Lord to him together with all who were in his house" (Acts 16:32).
10. The jailer and all his household were baptized, "having believed in God with his whole household" (Acts 16:34). The Bible doesn't specify the ages of those in his household, but they all believed in God.
It's bedtime in Korea.