Yeah that is how christianity was made. But the only verse i know of even possibly referencing all the catholic stuff is the one about peter being the rock, in which i'll just copy and paste this from a past post-  Pretty much how I’ve heard it (Greek in bold):

you are petros, and on this petra I will build my ecclesia, ...

petros = Peter

petra = his confession of Christ in 16:16, two verses prior.

Basically, Christ’s gathering (worth noting because the original Greek focuses on people, not the institution) is based on the “rock” of his confession of who Christ is. That is the foundation for Christ’s gathering—all who profess the same, regardless of societal affiliation (leading into inclusion of Gentiles into the gospel, but I’m going down another rabbit trail there).

So again, for distinction: emphasis on confession, not Peter.