The simple answer is that, just as faith was required in the Old Testament for individuals to please God and to be in relationship with him, so in the New Testament, when baptism "took off afresh" for the nation of Israel with John the Baptist's baptisms, and with what Jesus Christ said, then with how all the apostles explained their agreement with faith needed for genuine conversion, water baptism then being a public declaration that such faith had been expressed.
A good list of 12 such N.T. texts has already been provided in another answer, so I will not repeat them here. However, the idea of credo baptism first originating in 1609 with a Baptist denomination is totally wrong, plus misleading. For a start, credo baptism is reported in the N.T! Thereafter, the Christian Church continued to practice it, with Tertullian condemning an instance of infant baptism in 197. Despite that, sprinkling of infants gained ground. Here is what this Catholic authority says on the matter:
"The baptism of adults is presupposed throughout the NT and the early
Christian period... Infant baptism developed naturally out of the
entirely different circumstances in which Christianity found itself
when society had become Christian... But child baptism became the
normal practice from about the 4th or 5th century onwards... even
today, through the intermediary of their godparents infants are
treated at their baptism as if they were adult: they [the godparents]
renounce Satan, confess the faith, and state that they wish to be
baptized." Encyclopedia of Theology, p69, article by Burkhard
Neunheuser, Burns & Oates, 1961 [Emphasis mine]
This means that credo baptism was the single form of baptism until Catholicism approved this new practice later. It was based on the teaching that salvation was dependent on baptism, i.e. baptismal regeneration, (Sess. 7, Canons on the Sacrament of Baptism, 1-14, D 857-70) and that baptism could not be repeated. Groups that disagreed with this, saying salvation came first at the point of putting faith in Christ, were later declared to be heretics, and so the uprising of infant baptism caused them to be ousted from the Church.
There is written confirmation of this after 1348, but the fact that Catholicism declared credo baptism to be a heresy long before then shows that it was practiced by others. This means that trying to attribute credo baptism to either Anabaptists (twice-baptised) or to Baptists circa. 1609 is nonsense.
The new emperor, Charles IV, vigorously pursued (persecuted) all Christians who objected to such things as infant baptism. At that time, many people who had been baptised as babies or toddlers, later came to hear the gospel as proclaimed by Christian preachers outside of Catholicism, confessed Christ personally and were fully immersed in water. They were, effectively, the first Anabaptists, long before a particular group in Munster was named such, circa 1524. The Anabatist non-Christian excesses near the end of that century gave them a bad reputation, but their predecessors were virtuous Christians who would not accept Catholic dogma on such matters as infant baptism (and other issues.) They were all tarred with the same, one brush of 'Heretics'. All of them, from the 2nd century on, maintained that faith must be a condition of baptism. In this, they were simply sticking to the New Testament teaching, even though it cost many of them severe persecution, if not their lives. It predates Lutherism and Calvinism by centuries!