You haven’t left any other text apart from your question, so I need to nuance my answer in several ways to begin with. Firstly, it’s not particularly meaningful to talk about a ‘Catholic’ church if you mean modern Roman Catholic church, in the 1st century. At that stage there is no demonationalism, there is diversity but there isn’t really clear lines between this church, that church, and whatever. Secondly, the rise of the prominence of Rome as a church center occurs over hundreds of years, and in the 1st and 2nd century this is not really a feature. Thirdly, the word ‘Papa’ was used to refer to several bishops and leaders in the early church, and the distinctive idea of the bishop of Rome as ‘the Pope’ evolved much later. Indeed, if one is analysing the New Testament corpus, it’s quite difficult to even make the argument that there is much difference between an elder (presbyter) and a bishop (episkopos).

As for sources, most of our early ones suggest that Linus became the first ‘bishop of Rome’. Irenaeus, in Against Heresies 3.3.3 says that the apostles, “committed in to the hands of Linus the office of the episcopate”, in discussing apostolic tradition and succession of bishops with reference to Rome. Jerome’s Chronicon says that Linus possessed the Roman church, i.e. authority over it, after Peter, in 68 AD. Eusebius also states much the same, in Church History 3.2. A few other documents repeat the claim.

I would not go so far as to call him the ‘first pope’, but the documentary record suggests that by the 4th century Linus was considered the first bishop of Rome after Peter and Paul, even though we have very little evidence that Peter was ever in Rome, and no indication that Paul led the church there.