This is a very debated question.
According to the Catholic Church, when Jesus told Peter, "And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it," he was appointing Peter as the first Catholic Pope and instituting the Church. If this view is accepted, the Catholic Church began around 32 CE.
Others believe that in 312 CE when Emperor Constantine proclaimed he had had a vision to unite the Roman Empire under a universal (i.e. "catholic") church, this began the Roman Catholic Church. Others point to earlier dates (certain of the "Church fathers") or later dates (to Nicea or
In my opinion, the Catholic Church began on February 27, 380 when Emperor Theodosius issued his edict, De Fide Catolica, in Thessalonica, published in Constantinople, declaring Catholic Christianity as the state religion of the Roman Empire.
Following the destruction of Jerusalem in 70 CE the followers of Jesus, like the Jews, spread out through the known world. These people studied and prayed and sought God's direction according to their ability. Some of these people supported merging their doctrines with Roman Pagan
doctrines in an attempt to lessen the persecutions and gain official recognition by the Empire. Others doubtless supported this position out of lack of knowledge. They were Romans and they knew these teachings, but were ignorant of Jewish scripture and doctrine. In the New Testament Paul
and others warn that Pagan and other "heretical views" were being introduced into the Church. It can be argued that these Romanized teachings were included in these warnings.
Other people sought more mystical approaches (the Gnostics etc.). As time went by there were many "Christianities" not just one and these were incredibly diverse in their teachings and beliefs. Some Nazarenes believed one thing, others another.
Once the form of Christianity embraced by certain pro-Roman factions gained political power and recognition the Catholic Church began a long process of distilling and canonizing its beliefs into a Roman hierarchically authorized form. This form is what we today refer to as Roman Catholicism.
Other forms of Christian religion continued as well but these were forced underground by severe persecution. Sects like the Abegensians, Cathers, Arians, Anabaptists, the Coptic Church, etc. maintained their teaching as the arguably true Christian faith largely underground but by this point it was impossible to identify any as being truly apostolic (as the teachings of the Apostles). In time most of these were destroyed by the might of the Catholic Church or faded away and yet the Papacy never managed to completely destroy the other sects.
Eventually the Roman Catholic Church split into the Eastern and Western (Orthodox and Roman) Catholic Church, each claiming to be the original. Later of course the Church of England (Anglican) left the Roman Church and still later came the Protestant Reformation and so on. Each group claiming to be the restoration of the One True Church revealed by Master Y'shua. Which if any of these are the original is a matter of personal faith. At my Noahide Nazarene web site I present what I believe are most likely the original teachings.
This may be more information than you wanted to know, but it is relevant to what we know as Catholicism and Christianity.
If you have further questions feel free to write back any time.
~ Ben Ruach ha Kodesh
~ John of AllFaith