Baptism has it’s origins in the Jewish Rite of Mikvah, or ritual baths.
Most of the first baptisms were done by full emersion, just as the Jewish Mikvah was done by fully emersing oneself. In the case of baptism, the sacrament is adminstered by someone else, in Mikvah’s you enter the ritual bath, and immerse yourself. The water from a Mikvah must be “living water” that is water from a river or a stream. It cannot be water obtained from a city pipe, or other artificial sources. Jesus also called Himself the Living Water, and instructed the Apostles to Baptize.
While in the early Church most of the baptisms were done by full emersion, tehere were times and places where it could not be done, people who were sick and on their deathbeds could not be immersed, incolder climates like Northern Europe it wasnot possible to immerse in the winter time, and as baptism could not always be postponed until the warmer time, pouring or sprinkling the waters of baptism were allowed, and held as valid. From the earliest days of the Church either sprinkling, pouring or immersing were all held as valid. In the Eastern Churches, Immersion is most common, although they hold sprinkling and pouring as valid.
Many Latin Rite Churches have re-instituted full immersion, but unlike some Protestant sects they who have rejected all but full immersion, the other two forms are still accepted among Latin Rite Catholics.