John 20:30-31 30 Now Jesus did many other signs in the presence of the disciples, which are not written in this book; 31 but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.
Now that he has found salvation, he would continue to read this NT to find out how to serve and worship the Creator, his God, his Saviour. How to live his Christian life. He would then discover what the future of this world holds for those who are not saved. And he would learn that God's wrath will be poured out one day on an unbelieving, Christ-rejecting world. Then that same Christ is going to return and set up His kingdom just as He promised in Matthew, Mark, Luke, and John. He is thoroughly equipped with the intended purpose of the Bible:
"All Scripture is given by inspiration of God and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work." 2 Tim. 3:16,17.
Now suppose he sets out to find like-minded believers, to share his Christian life with. He finds a beautiful Church and decides to enter. What does he find? An empty pew where he watches priests celebrating the Mass, hearing confessions, and leading in the praying of the rosary before a statue of Mary. He searches his Bible, certain he must have missed all this. But no, it is not there. Confused, he asks someone to explain this mystery, not in the Bible, but performed by so many.
He's told about baptismal regeneration and justification, programs that last a year for the preparation of justification, seven sacraments, sanctifying grace, transubstantiation, a continuing sacrifice, confession to a priest, temporal punishment, indulgences, purgatory, merited eternal rewards, priestly ordination, the papacy, ruling bishops, the Magisterium, Mary's Immaculate Conception, her Assumption into Heaven, her co-redemptive work, and her mediation of all grace.
This new creature in Christ would have two choices. Knowing that these beliefs were not only NOT taught in Scripture, but actually contradicted God's Word, he could put his Bible aside and begin the journey to salvation through this RCC, or he could simply take his Bible, thank God for the simplicity that is in Christ, and move on.
For some, there are never enough proofs. For others, God's enduring word is proof enough.
John 20:30-31 does not say so. It says that the scripture is sufficient to produce faith in some ("may believe"), and that among those who do believe, some "may have life".