C'mon...really?
The word "catholic" -- small "c" -- originally simply meant "universal"...as in the universal church.
I suppose had they had it in mind to use a parallel phrase back then...say "The Body of Christ at-large"...and then had several hundred years later a large Christian segment calling itself "The Body At-Large" emerged... you can't just simply say that anybody using the phrase "Body at large" before that segment of the church arose was automatically members of same-said church.
Now do I regard Catholics as part of the overall Body of Christ? (Yes) Are they part of the "universal church"? I believe so. Does that make them the "only game" in town? (No)
Let me provide yet another parallel, this one from the 20th century: The National Association of Evangelicals arose about 1942. A merger of two denominations brought about the Evangelical Free denomination in 1950.
Evangelical Free members can't begin to go about saying that because they are Evangelical Free, and because Evangelicals widely emerged in 1942, that anybody who called themselves "Evangelicals" in '42 were also somehow automatically Evangelical Free members...especially when that specific denomination was officially formulated AFTER the fact!
Yet that is tantamount to what you are trying to do...
Sure I can because I don't buy the notion that the RCC emerged in the 300s. In my research I found numerous historical witnesses showing the continuity of the Catholic Church before and after the 300s. You are as free to reject those sources as I am to accept them.
Peace be with you.