Your difficulty is that you perceive that Catholicism is a denomination like any other. It is not.
It is the Church that Christ Himself founded, entrusted to the Apostles, who then entrusted it to the Apostolic Fathers, the Church Fathers, and down through the ages to today.
And that claim is provable. Because Lutherans did not exist before Luther, Calvinists did not exist before Calvin. But Catholics were present from the beginning.
Here you present it rhetorically, and that presentation shot full of unspoken assumptions.
I've examined the argument (and the various claims) and found more holes in the argument (particularly when exclusivity is included, along with infallibility of so-called Magesterium, those two logically enough needing both exist, and be complimentary, or else everything comes rather unwound) ---than solid support, and have otherwise also enjoyed having the Lord introduce Himself to little 'ol me in very powerful, unmistakable ways. Unmistakable, for my own self, others need not necessarily have the exact experiences with Him as have I...
That claim is not as provable as Catholics would like to presume. The tenets of the faith are what Jesus entrusted to the Apostles who then passed it down to others and which the Holy Spirit ensured was written down - just as He had with the ancient people of Israel. It is the truth that never changes - because it IS the truth and truth is absolute. But when people - as people are wont to do - fiddle with what God has said and put in their own spin, trying to reason out carnally those things that are spiritually discerned, the truth can get twisted. It sure happened with Israel and brought down God's judgment upon them. We already know that the "church fathers" often disagreed with each other and didn't always stay faithful to the faith once delivered unto the saints so they aren't any greater authority than Scripture. It's the SAME Holy Spirit who leads us into all truth as who led those ancient believers.
Where modern day Catholics err is in claiming that the "church" which Jesus established is THEIRS rather than it always having been that spiritual house of which EVERY believer is a living stone joined together throughout time to make up the called-out assembly (ekklesia) which is Christ's body, His bride. It is the continuity of belief in the tenets as taught from the start that determines whether or not one is part of Christ's church and NOT simply some boastful assertion that "WE" are that church just because the adjective small "c" "catholic" (meaning universal) was first used in the second century to mean the whole faith tradition and co-opted as a proper noun for an organization that gradually rose to power.
So, no, "Lutheran" nor "Calvinist" nor "Baptist" nor "Presbyterian" as called by those names may not have existed from the beginning but neither did "Catholic" or "Orthodox", for that matter. To be a member of THE church, one must believe in the Apostolic teachings PERIOD. Better get used to having brothers and sisters in Christ - eternity is forever!