Was the immersion in water by the hand of others, a part of joining Christianity?

The question is specifically asking if the benefits of baptism can only occur if another person does the immersion.

It would seem that for John's baptism into repentance, a person could study John's teaching about the need for repentance, then baptize himself to show God and the world that he is prepared to throw away his past beliefs and prepare himself for something new.

BUT to be baptized in the name of Jesus as a symbol of joining the Body of Christ, the person would have to be guided into it by somebody who has already learned what it means. If the person chooses to study Christianity long enough to figure it all out on his own and then baptize himself in private, he will likely learn things incorrectly because God's Spirit is not teaching him. So he will baptize himself into a lie.

A basic truth of Christianity is that a person cannot be alone and selfishly define things on their own terms, they must humbly accept guidance from God and elders in the Church. Allowing a more senior member of the church to immerse them requires some humility so it is a good symbol of that. It also gives the person doing the immersing a chance to show love to the newer member by guiding him in the truth. God wants His children to assemble together and He likes it when we learn our gifts and share them with each other.

A person should be baptized early in their relationship with Christ, before they have learned what it actually means to call Jesus "Lord" or even understand what believing in Him really means. The Ethiopian eunuch studying the book of Isaiah (Acts 8:26-40) could have rebuffed Philip and said he didn't need help understanding it. But he knew he needed someone to guide him (likely because God had attracted him with a bit of faith to get started). This led him to learn about baptism into Christ and wanting Philip to do it for him right then.

The basic answer is yes for full immersion baptism but not necessarily always "by the hand of others." However, this does not mean that sprinkling wasn't also used. Evidence for immersion baptism is found, even before the advent of Christianity, in the Jewish tradition for Gentile converts. This tradition was probably inherited by the earliest (pre-Pauline) churches, since they saw themselves not as a new religion, but as Jews who had found the Messiah.

Immersion

The Jewish Ecyclopedia informs us that Jewish baptism was understood

as a religious ablution signifying purification or consecration... The Rabbis connect with this the duty of bathing by complete immersion ("ṭebilah," Yeb. 46b; Mek., Baḥodesh, iii.).. these three acts [washing one's clothes, sprinkling with blood and full immersion in flowing water] being the initiatory rites always performed upon proselytes, "to bring them under the wings of the Shekinah" (Yeb. l.c.).

The tradition of water baptism in a flowing stream was also used by John the Baptist, but administered to Jews, not converts to Judaism. The disciples of Jesus, several of whom had followed John previously, certainly inherited the tradition from him.

Hands

The J.E. article continues:

Baptism, next to circumcision and sacrifice, was an absolutely necessary condition to be fulfilled by a proselyte to Judaism (Yeb. 46b, 47b; Ker. 9a; 'Ab. Zarah 57a; Shab. 135a; Yer. Kid. iii. 14, 64d)... The next ceremony, adopted shortly after the others, was the imposition of hands, which, it is known, was the usage of the Jews at the ordination of a rabbi.

The laying on of hands was another ceremony adopted by those Jews who followed Jesus and later inherited by Christianity. But regarding baptism itself being administered only by the hand of another, as opposed to by oneself, this is less certain. Jewish ritual baths are entered by oneself, but with a witness, whose function is to declare the rite properly accomplished. On the other hand, John 4 reports

Now when the Lord [Jesus] knew that the Pharisees had heard that Jesus was making and baptizing more disciples than John (although Jesus himself did not baptize, but only his disciples), he left Judea and departed again to Galilee.

Since the text specifies that Jesus himself did not participate, we may understand that the disciples did take an active role in baptizing new converts. In other words, they assisted converts manually. The most likely method would be to use the same as John's, immersion in flowing water. However, since in the Jewish rite the laying on of hands is a separate rite, as it was in early church, there does not seem to be any particular significance to touching as part of baptism. It is the water, not than hands, that is important.

Although being baptized by another [either standing by or manually assisting] was probably the norm, we do know of at least one Christian saint, Thecla, who baptized herself. Facing martyrdom with having been baptized:

...when she had ended her prayer, she turned and saw a great tank full of water, and said: Now is it time that I should wash myself. And she cast herself in, saying: 'In the name of Jesus Christ do I baptize myself on the last day.'

Thecla's case was accepted by the church as a special in extremis situation but self-baptism was definitely not the norm, both because it was by this time frowned upon, and because she was a woman; and therefore not qualified to administer the rite.

It should be noted that although the earlier examples provide evidence for full-immersion baptism "in the time of Jesus in Judea" this does not mean that sprinkling was not practiced as well. Sprinkling and hand-washing were part of the Levitical purity rites, and the prophet Ezekiel had declared: "Then will I sprinkle clean water upon you, and ye shall be clean." (36:25)

From the above we know that full-immersion baptism was practiced by converts to Judaism in Judea, and this is the likely source of Christian baptism as well. Converts were manually assisted by a minister in Christian baptism, but this was probably not a necessary part of the rite.

Be aware that the followers of Christ Jesus were not known as Christians till around 47 C.E. (Acts 11:26) after the death and resurrection of Christ Jesus. But even before then, water baptism by immersion was practiced in Judea by John the Baptist, the cousin of Jesus. John prepared the way for Christ by calling people to acknowledge their sin and their need for salvation. His baptism was a purification ceremony meant to ready the peoples’ hearts to receive their Saviour.

In Matthew 3:11, John the Baptist mentions the purpose of his baptisms: “I baptize you with water for repentance.” Paul affirms this in Acts 19:4: “John’s baptism was a baptism of repentance. He told the people to believe in the one coming after him, that is, in Jesus.” John’s baptism had to do with repentance—it was a symbolic representation of changing one’s mind and going a new direction. “Confessing their sins, they were baptized by him in the Jordan River” (Matthew 3:6). Being baptized by John demonstrated a recognition of one’s sin, a desire for spiritual cleansing, and a commitment to follow God’s law in anticipation of the Messiah’s arrival. https://www.gotquestions.org/baptism-of-John.html

In John 1:19–28, we are introduced to John the Baptist, the rough and rugged prophet who was spreading the news that Israel’s promised Messiah was coming. The religious leaders had begun to question John, “Who are you?” Since John was baptizing people, the Pharisees demanded to know by what authority he performed the baptisms. John answered that he was merely the one sent by God to prepare the way for the Lord. Soon Jesus would take the stage and begin His earthly ministry by being baptized. The gospel writer explains, “This all happened at Bethany on the other side of the Jordan, where John was baptizing” (John 1:28). The Bethany where Jesus was baptized is on the other side of the Jordan, on the east bank of the river (John 1:29-34). https://www.gotquestions.org/where-was-Jesus-baptized.html

Jesus commanded that his disciples baptise others by water immersion: “Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit” (Matthew 28:19).

With John’s baptism, a person repented of sin and was therefore ready to place his faith in Jesus Christ. With Christian baptism, where the one being baptised is lowered into the water and then raised back up, they now identify with the death, burial and resurrection of Christ Jesus. It is not about “joining the Christian religion” or saying a person is now a Catholic, or a Protestant. It is about dying (symbolically) to a previous sinful life and being born again (spiritually) as a person who follows Christ and who now belongs to Him.

For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus. (Galatians 3:27-28)

So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God, (Ephesians 2:19)

EDIT: The word “baptize” comes from a Greek word which means “to submerge in water.” Baptism by sprinkling or by pouring water over someone is an oxymoron, or self-contradictory. In order to fully submerge an adult under water and then bring them up, at least one, if not two, persons are needed to lower and raise the baptismal candidate and assist in making sure no water will be breathed in.

As for laying hands upon the baptised person, this is a common practice. When I was baptised, the minister simply placed his hand on my head, quoted from 1 Corinthians 12:13 “We were all baptised by one Spirit into one body”, and made this prayer:

We pray, our Lord and God, that you would overshadow Lesley and lead her into more light and freedom, and that she will find her place in your body and be equipped for your service.”

A few weeks after my baptism, in answer to prayer, I received confirmation through the Holy Spirit that I had been adopted into God’s family and was assured that I now belonged to Christ. This is an important distinction to make because some people mistakenly think that baptism means they now belong to an organisation.

I hope this helps to address the main point of your question.