AD 30 was the beginning of the papacy of Peter the Apostle, which according to the Catholic Church, was its first pope. Catholic teachings state that Peter’s successors form an unbroken line of Church leaders from AD 30 to the present day, though historic evidence is somewhat incomplete. This is the canonical start date of the Catholic Church as an organisation. “Christianity”, broadly speaking, is just a label affixed to anyone who identifies themselves as a follower of the teachings of Jesus Christ.

The Catholic Church names Jesus Christ as its founder. If you accept this claim, then you could definitely say that it was a political organisation as well as a religious one from the beginning, as Jesus was notoriously put to death by the Roman state for political reasons. The Jewish Sanhedrin which had condemned Jesus for claiming to be the Messiah had no legal authority in Roman Judea; legally speaking, Jesus was put to death on the orders of Pontius Pilate (prefect of Judea) for sedition and for being “King of the Jews”. The legal veracity of this charge is questionable, of course, and Jesus famously preached for his followers to “render unto [the Emperor] the things that are [the Emperor’s]”, i.e. to respect the state and the laws, but the Roman Empire wasn’t known for being an egalitarian state with strong rule of law.