Some Believers think that this immersion should take place immediately following a person's confession of faith in Christ - as per the examples in the Book of Acts.
This idea needs a bit of thought.
For instance, those early Believers on the Day of Pentecost were aware of the teachings of the Hebrew Bible. In addition, they were all adults with adult responsibilities and accountabilities.
And they knew that being immersed could result in serious persecution or even death for them. (As it for many Believers in some parts of the world today.)
In addition, there are the unbelievers' misunderstandings and false accusations. In one place it was claimed that:
"... these are all acting contrary to the decrees of Caesar, saying there is another king - Jesus," Acts 17'7.
Nevertheless, they were/are still immersed.
Elders are responsible for ensuring that those who desire to be immersed in water are convinced and understand what it is they are entering into.
For instance, those who have grown up among the Believers may feel they ought to be immersed.
Reasons for immersing someone, such as to help them overcome spiritual problems or to help personal needs, etc, are wrong reasons.
However, asking them about their understanding of repentance, faith toward God and their kind of spiritual experience with gentle questions could help them.
For someone the issue could be: is it of their own free will that they are asking? It may be because others are being immersed or because someone has told them they should.
Above all, no one should have the idea that being immersed in water saves them.