The book of Acts, in the Bible, gives us several examples of baptism. In five of these we observe that baptism was done as soon as possible after someone believed in Jesus Christ. Baptism was not delayed.
Soon after Jesus ascended to Heaven, Peter preached the gospel in Jerusalem on the day of Pentecost. About 3000 people received and believed the gospel that day. They were told to "repent and be baptised, every one of you..." (Acts 2:38)
Their baptism was important. It was "for the forgiveness of sins" and to "receive the gift of the Holy Spirit" (Acts 2:38-39).
Peter urged them to "be saved from this perverse generation". They were not yet saved. (If they were already saved, Peter would not have said, "Be saved...") They needed to "repent and be baptised" (Acts 2:40, 38).
Therefore we would not expect their baptism to be delayed by days or postponed for weeks. And, indeed, it is said that "those who gladly received his word were baptised, and that day about 3000 souls were added" to the church (Acts 2:41-47)
So we see no postponement of baptism for those who were being saved. They received and believed the gospel, repented of their sins, were baptised, received forgiveness and the gift of the Holy Spirit, and were added by God to his church. All this within the day.
On subsequent days more people were being saved "daily" in the same way. There was no delay (Acts 2:46-47).
There was a man from Ethiopia, who ranked highly among the servants of his Queen. He had been to Jerusalem to worship God, and was riding home in his chariot. He was reading Isaiah 53.
Philip approached the chariot and called, ""Do you understand what you are reading?" The Ethiopian didn't understand, so he invited Philip to enter the chariot and explain the passage. Philip preached Jesus to him (Acts 8:26-39).
As they went on their way the Ethiopian saw some water by the road and he said, "Here is water; what hinders me from being baptised?" Philip said that nothing hindered him if he truly believed what Philip had shown him.
The Ethiopian said that he did believe, so he stopped the chariot and both he and Philip went down into the water and Philip baptised him (Acts 8:26-39).
It is evident that Philip proved from the scriptures that Jesus is the Christ, the Son of God. It is also evident that Philip included baptism in his message. The Ethiopian saw reason to obey this command immediately, so he did not go past the water. He commanded the chariot to stop so that he could be baptised then and there.
Paul (previously named Saul) was in Philipi with Silas. They got into trouble because Paul cast out a demon from a slave girl, and her masters could no longer profit from the divinations the demon had provided (Acts 16:16-19)
Paul and Silas were beaten severely and thrown into prison. However an earthquake caused all the locks to open and the prisoners’ chains were loosed. Yet the prisoners remained inside. None fled. This saved the jailer’s life and he became a Christian (Acts 16:34).
Paul and Silas spoke the word of God to the jailer and all his household and they believed the word that Paul and Silas preached. The jailer "took them the same hour of the night and washed their wounds, and immediately he and all his household were baptized" (Acts 16:29-32).
One might think that, under the circumstances, the baptisms could wait till morning. Yet the baptisms took place immediately, "the same hour of the night" (Acts 16:33)
Paul came to Ephesus, and found some disciples of Christ. But they had been baptised only by John’s baptism and did not know about baptism in the name of Jesus to receive the Holy Spirit. Paul explained it to them. "When they heard this, they were baptized in the name of the Lord Jesus" (Acts 19:5 NKJV)
These disciples were baptised when they heard about their need for baptism into Christ. They obeyed forthwith. There wasno delay.
Paul recounts his own conversion. He was on his way to Damascus to persecute Christians. As he approached the city, Jesus appeared to him and made him blind. In Damascus, Ananias visited him, healed his blindness, and told him that he was chosen to be a witness for Christ (Acts 22:6-16)
Ananias said to Paul (then known as Saul), "And now why are you waiting? Arise and be baptised, and wash away your sins, calling on the name of the Lord" (Acts 22:16 NKJV).
Saul had not yet had his sins washed away in the blood of Jesus because he had not yet been baptised into Christ's death (Romans 6:3-4).
There was no reason for Saul to delay, and every reason to arise and obey. Thus Ananias urged Saul to be baptised straight away.