The first believers were called Catholic ye universal church ye community of Jesus. That was before they got the exonym Christian.
And yes, they started off with a Pope, Peter, right from the start, the foundation of the Catholic church in 33 AD at Pentecost
The term “Catholic” (from Greek katholikos, “universal”) was used by early Christians to describe the Church’s unity across geographic and cultural boundaries. St. Ignatius of Antioch, writing around 107 AD to the Smyrnaeans (one of the seven churches!), says: “Wherever Jesus Christ is, there is the Catholic Church” (Letter to the Smyrnaeans 8:2). This early use shows that even the churches in Asia were understood as part of the universal Church, united by bishops in apostolic succession.