According to Catholic apologist and philosopher Michael Liccione:
As a Catholic, I’d say that of course the Catholic doctrine of the papacy cannot be “demonstrated and sustained” just by “Scripture itself,” even though it is supported by Scripture when Scripture is interpreted in a certain way. Indeed, from what Vatican II said, we may infer that no article of faith can simply be “demonstrated” by Scripture; for “Scripture, Tradition, and the teaching authority of the Church are so linked…that none can stand without the others” (Dei Verbum §10).
So, by Liccione’s admission, not a single Catholic dogma can be demonstrated by Scripture alone. Source