It is really simple actually. It is a matter of history. Thus, it can be proved or disproved based solely on that.
If there was another Church besides the Catholic Church in early Christianity then tell me what it is. If you can't then I am not surprised. However, I can give you historical facts that show the Catholic Church existed as the early Church. You can read for instance the writings of the early Church Fathers, the Apostolic Fathers. The Apostolic Fathers are called Apostolic because they lived during the lifetime of the Apostles.
St. Ignatius, Apostolic Father, Bishop of Antioch (where they were first called Christians - Acts 11:26), and student of John the Apostle, wrote in AD 110:
"Wherever the bishop appears, there let the people be; as wherever Jesus Christ is, there is the Catholic Church. It is not lawful to baptize or give communion without the consent of the bishop. On the other hand, whatever has his approval is pleasing to God. Thus, whatever is done will be safe and valid." — Letter to the Smyrnaeans 8, J.R. Willis translation.
On the matter of the Eucharist he wrote what is consistent with Catholic teaching:
"Take note of those who hold heterodox opinions on the grace of Jesus Christ which has come to us, and see how contrary their opinions are to the mind of God. . . . They abstain from the Eucharist and from prayer because they do not confess that the Eucharist is the flesh of our Savior Jesus Christ, flesh which suffered for our sins and which that Father, in his goodness, raised up again. They who deny the gift of God are perishing in their disputes."
— Letter to the Smyrnaeans 6:2–7:1
Ignatius wrote a number of letters that describe the importance of following the Bishop. For example:
"Take care to do all things in harmony with God, with the bishop presiding in the place of God, and with the presbyters in the place of the council of the apostles, and with the deacons, who are most dear to me, entrusted with the business of Jesus Christ, who was with the Father from the beginning and is at last made manifest."
—Letter to the Magnesians 2, 6:1
Ignatius warned against falling away to strange doctrines, ie. things not orthodox and contrary to the Church's teachings on things like the Eucharist or practicing the Lord's Day:
"Be not seduced by strange doctrines nor by antiquated fables, which are profitless. For if even unto this day we live after the manner of Judaism, we avow that we have not received grace.... If then those who had walked in ancient practices attained unto newness of hope, no longer observing Sabbaths but fashioning their lives after the Lord's day, on which our life also arose through Him and through His death which some men deny ... how shall we be able to live apart from Him? ... It is monstrous to talk of Jesus Christ and to practise Judaism. For Christianity did not believe in Judaism, but Judaism in Christianity"
— Ignatius to the Magnesians 8:1, 9:1-2, 10:3, Lightfoot translation.
Due to space I can not write much more except to say there are many Church Fathers who have written about the Catholic Church and the need to follow it as Christ's Church, lest one fall away into error. If there was another Church where is it? We have no record of it? The Churches that Paul and Peter went around establishing in Acts, like Rome, Corinth, Antioch, etc. These are the beginning of the Catholic Church. There wasn't one church in Acts and then all of a sudden the Catholic Church. No, where do you think the Catholic Church comes from, but from these same churches started by the apostles?
The Pope for instance has Apostolic Succession to St. Peter. That means we can trace a line of bishops all the way back to St. Peter.
As far as Jesus being real. Do you really think that people would go around spreading an imaginary Jesus, dying for an imaginary Jesus, and that an imaginary Jesus would be so successful that billions of people around the world would claim to believe in him? It doesn't make sense. Occams razor - the simplest solution says that with so many people that believe in him and even die for him, then he must be real.