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Rather than reinvent the wheel, I will provide you links to some Catholic Answers materials, including the tract “Proving Inspiration” re: the Bible, and this article Tim Staples, which illustrates the historical linkage between the Old Covenant Kingdom of Israel and the New Covenant Israel founded by Jesus—the King of Kings—on “St. Peter the Rock” and his papal successors.
In addition, no serious scholar questions whether people like Moses and King David existed in Old Covenant times, let alone Jesus in New Covenant times. They will take issue with whether God guided ancient Israel and whether Jesus himself is God. So whether Judaism and Catholicism are not simply historically verifiable but truly of God is not something a historian has the competence to evaluate. But God provides various “motives of credibility” (CCC 156) to aid believers and prospective believers.
In addition, regarding Catholicism—in particular in light of the Bible—see the excellent Catholic Answers primer on this matter—Pillar of Fire, Pillar of Truth, as well as the Catholic Answers tract “Scripture and Tradition.” You may also wish to examine further resources noted in this Catholic Answers article.