Batism at the time of Jesus and shortly after would have been based on the Jewish Mikvah purification bath.
A Mikvah purification bath would have been done with living water, that is to say running water as opposed to stagnant water. The person would strip naked go down into the water, spreading their fingers, opening their eyes, and keeping their mouth wide open so that the water would touch every possible part of their body, thus immersing themselves completely. This is what was done when in the Bible God tells Israel to "Purify yourselves." The phrase "Wash your garments" was an idiom for undergoing a ritual Mikvah purification bath.
The mikvah is still used by the Jewish faith. A good article about it is at *chabad.org/theJewishWoman/article_cdo/aid/1541/jewish/The-Mikvah.htm*
The Mikvah was a rule of the Law of Moses as part of the old covenant. The Mikvah was specified by God and Solomon included a Mikvah pool in the temple for the priests.
He also made the molten sea. It was perfectly round, ten cubits in diameter, five in depth, and thirty in circumference; below the rim a ring of figures of oxen encircled the sea, ten to the cubit, all the way around; there were two rows of these cast in the same mold with the sea. It rested on twelve oxen, three facing north, three west, three south, and three east, with their haunches all toward the center; the sea rested on their backs. It was a handbreadth thick, and its brim was made like that of a cup, being lily-shaped. It had a capacity of three thousand measures. Then he made ten basins for washing, placing five of them to the right and five to the left. Here were cleansed the victims for the holocausts; but the sea was for the priests to wash in. (2 Chronicles 4:2-6)
The Mikvah is what John the Baptist was doing. John was performing Mikvah purifications in the living water of the Jordan River. The people realized according to the prophecy of Daniel that the Messiah was coming soon, and so people were coming from all over Judea to the lowest spot on earth, out in the middle of the Judean wilderness, to confess their sins and undergo a Mikvah purification bath.
**At that time Jerusalem, all Judea, and the whole region around the Jordan were going out to him and were being baptized by him in the Jordan River as they acknowledged their sins. *(Matthew 3:5-6)*
When the Bible says that Jesus was "baptized", they are talking about a ritual Mikvah purification bath. Jesus also went into the wilderness to undergo the Mikvah, and in undergoing the Mikvah of the old covenant, Jesus elevates it to supernatural status - to sacramental status of the new covenant.
**After Jesus was baptized, he came up from the water **and behold, the heavens were opened for him, and he saw the Spirit of God descending like a dove and coming upon him. (Matthew 3:16)
The Christian sacrament of baptism was the new sacramental form of the Jewish Mikvah, and it was done by immersion in the earliest Christian communites. The OP's friend is correct that the earliest Christians preferred baptism by immersion in in "living water".
Some Catholic Churches Churches have fountains and other ways to produce living or running water and still practice baptism by immersion. Catholics also pour the water, thus fulfilling the requirement that it be running water.
If you read the requirments of the Mikvah in the article linked, you will see that it has to be water from a natural source - rain water or taken directly from a stream or river. It cannot be tap water so both Catholics and non-Catholics don't really fulfill the basic requirements of the Mikvah upon which baptism is based and which Jesus underwent. But that's not really the point.
Catholics believe that the Catholic Church was established by Christ and given the authority of Christ, and so we believe the Church gets to decide what constitutes a valid baptism. Pouring of water and trinitarian form meets the basic requirments for baptsim according to the Church.
The earliest known worship guide is called the Didache. The Didache was written in the late first or early second century, within 100 years of Jesus' ascension into heaven, and it records some of the basic ideas held by the earliest Christians as well as some basic instructions on Christian worship including how to properly baptize.
**Chapter 7. Concerning Baptism. And concerning baptism, baptize this way: Having first said all these things, baptize into the name of the Father, and of the Son, and of the Holy Spirit, **in living water. But if you have no living water, baptize into other water; and if you cannot do so in cold water, do so in warm. But if you have neither, pour out water three times upon the head into the name of Father and Son and Holy Spirit*. But before the baptism let the baptizer fast, and the baptized, and whoever else can; but you shall order the baptized to fast one or two days before. *
So the earliest Chrisitans understood baptism by pouring water on the forehead to be valid. The Didache is actually fascinating to read. The whole thing is at earlychristianwritings.com/text/didache-roberts.html.