He calls himself the “bishop of Syria” in Romans chapter 2. He uses the term “Catholic Church” (or “catholic church” if you prefer — the original Greek text had no capitals) in several places, most notably in Smyrnaeans. I recalled a quote where he connected the two, but maybe my memory is faulty. I’d have to consult my books at home to be sure.
To capitalize on the capitalization of Catholic to infer that all Christians were “Catholics” back them is erroneous.
It wasn't until about 3 centuries later that Catholicism was actually put into existence, and then the retroactive designating of “Popes” starting with Peter.
No mention of “Popes” in the Bible.
Bishops, yes many times.
And as on poster stated, rapture isn't in the Bible so we apparently can't say it is Biblical. Must be the same for pope.