It is common for Catholics to deceive converts based upon history, it isn't what they say always but what they leave out of their propoganda that is misleading. The Catholics did come from the true church in a round about way,but were not the true body. They came from those who left the true apostles and fanned out into the world. That is how they became "universal" in a sense as a group of bodies filling the world. These bodies remained independent for a long time until joined into one group through church councils.
Catholics formed from multiple false theologies, that is why they had multiple votes on many subjects. Even the church Fathers were aligned with these theologies on occasion and influenced by them. John and I John can help trace the evolution. Catholics want you to believe in one pure body existing for centuries until the protestant reformation, but this isn't sustainable. Early in the 1st century there were already men and groups leaving the Apostles and forming bodies that denied or altered key truths. Don't let Catholics deceive you. Consider I John 2
1 John 2:19
They went out from us, but they were not of us; for if they had been of us, they would [no doubt] have continued with us: but [they went out,] that they might be made manifest that they were not all of us.
It is evident there were already false groups in the world and there are many passages supporting this fact. Catholics tend to think these all died and disappeared while only the Catholic remained. At the time Catholic wasn't formed yet and no body wore this formal name. It is an adjective not a name. What occurred is the true and false grew together and both survived.
In the 2nd and 3rd centuries various writers and councils sprang up to help create a singular theolog, this proves the false bodies were not all the same and they had many theologies they wanted to address, but many of these were just groups of false bodies. The groups voting were those who had left the Apostles. Consensus voting, if based upon what is false can't declare truth 100 pct. Following the masses isn't always the method. Voting where a majority of voters were never apostolic by reason of leaving isn't the best way.