I agree, at the end of the day we can’t “prove” God exists, and, without a time machine, we can’t be 100% certain of anything- neither Protestants or Catholics.
For Catholics who’ve done the digging, we found a (sometimes shocking) amount of evidence that gives us reason to believe the Church has always been Catholic, as Catholic as it is today. These reasons serve to inform our faith in a similar way that we might argue the complexity of the human brain informs us that we didn’t just pop up out of the mud somewhere a billion years ago.
If I read multiple books about Church history and the development of Christian doctrine that all draw the same conclusion- that the early Church was "C"atholic- I can either stop there, accept it and hit the Easter Vigil, or I can say, “Ok, there’s a claim from some historian. Show me how he drew these conclusions.” And you look at the documents he cites to be sure he’s not misrepresenting what these men 2000 years ago wrote, you do some digging to see if he’s a credible historian and scrupulous with his work. You reduce the claims as far as you can, like you said, until you hit a wall. And then you have to make a decision- is this reasonable? Not is there definitive, hard proof, for which we have very little of for any historical matter. Simply asking, based on the evidence available (which there is a lot of), are the Churches’ claims, at the very least, reasonable?
A lot of us have concluded that not only is it reasonable and probable, its also far more reasonable and probable than Protestantism being representative of the Early Church.
That’s why there is a disconnect when you say you “know” by faith, as we do. We believe our Faith is informed by reasonable evidence to be Catholic, which is why we are disatisfied with some of your responses (again, it isn’t directed personally at you).