Two steps:
First, by examining the motives of credibility and arriving at the conclusion that the Roman Catholic Church is the Church founded by Christ. This can be achieved by the use of reason, and quite easily with the help of actual grace.
Second. By accepting that what the true Church teaches is true. Since the Church teaches that the magisterium is an infallible teacher, it follows that if the Church infallibly proposes a doctrine as having been revealed by God, the person will believe that the doctrine in question is revealed - and they will believe it, not based on their private judgment, but on the infallible authority of the infallible Church teaching.
That is how a non-Catholic comes to believe that there is an infallible teacher that has infallibly taught a doctrine that was revealed by God.
This is absolutely correct. THIS is where private judgement has a legitimate role, in examining the motives of credibility. Traditional Catholics look at the Conciliar counterfeit Church and recognize that it lacks the Marks or Notes of the One True Church found by Christ. It's about a bigger picture than quibbling over the precise limtis of infallibility. In its doctrine and its publish worship, it is simply unrecognizable as those of the Catholic Church.
If you were to time-warp St. Pius X to today and have him behold Berogligo and his teachings and watch the Novus Ordo Mass being celebrated, would he recognize it as the Catholic Church? Absolutely not. THAT is what the question is here. I've long prescinded from debating about whether this, that, or another isolated doctrine is true or false. God does not expect the average Catholic to be a theologian, but He taught that the sheep that are of His fold recognize the voice of their Master. We do not recognize the voice of Our Lord in this counterfeit imposter Church. That is how most Catholics become Traditional Catholics, not by reading theology manuals and studying the text of Vatican II, but by their
sensus Catholicus informing them that, "this thing, whatever it is, is not the Catholic Church."
I became a Traditional Catholc after reading St. Alphonsus for the first time. I simlply compared the
sensus Catholicus behind his writing with that of the Novus Ordo and recognized instinctively the massive contradiction, that there were two essentially different things here. At the time I knew precious little about what was in Vatican II.