An anti-Catholic I know claims that the Catholic Church cannot, even in principle, admit that there are groups of non-Catholic Christians that have survived from the first century. He claims his church is one of these.
He's wrong on both counts. First, the Catholic Church could admit the existence of other groups of Christians which had survived from the first century if any still existed, but none do. All of the heretical groups that split off in the first century died out. Anyone who claims that there was a line of doctrinally Protestant people going back through history to Jesus doesn't know Church history.
Second, while some groups, such as the Baptists, sometimes make this claim, they claim descent from heretical groups such as the Montanists (a false-prophecy movement that said the New Jerusalem would descend in Phrygia, on Montanus's home town), the Donatists (who said sacraments are efficacious only if they are administered by someone in a state of grace), and the Albigensians (who said there are two gods, a good god who loves us and an evil god who made the world). There is simply no way that these groups were Baptists under a different name.
Also incorrect is the notion, seriously offered by some Baptists, that the Baptists are descended from John the Baptist--otherwise, why else would they sport his title?
(This argument is analogous to the one given by ministers of the Protestant denomination that calls itself the Church of Christ. They say theirs must be the original Church because the name of the Church founded by Christ could be nothing other than "the Church of Christ." Naturally enough, this argument has not found favor with people who do not belong to that denomination.)
The Baptists are a late offshoot of the English Reformation. Their denomination was started in 1609 by a British man named John Smyth, who was living in Holland at the time. He and his congregation of expatriate Englishmen began the first Baptist church, which later relocated to England, which is why all the early Baptist confessions were drawn up in that country.
Incidentally, the original Baptists practiced baptism by pouring (affusion) instead of dunking (immersion), although most of them today vigorously deny the validity of baptism by pouring. The founder of the Baptist Church in America, Roger Williams, finding no one qualified to baptize him, decided to baptize himself in 1639.