Catholics love to argue for the the legitimacy of their church from history. Here is a classic, but older example.
"Why are Protestants so much prejudiced against the Catholic Church, and why is it so difficult to convert them? It is because from infancy the minds of their children have been impressed with a false view of the History of their Religion—a Religion that dates only from the beginning of the sixteenth century. Why should not Catholics with equal, and even greater, effect confirm our children in their attachment to the Church, by showing them how to trace her to the times of the Apostles, and even to the Creation of the world? Is it not, then, of the greatest importance to teach them, together with their catechism, the History of their Religion? History is a safeguard against internal doubts, and a bulwark against all external attacks. He who has, by this means, been fully strengthened in his conviction that the Catholic Church is from God, and that she is the Only True Church, cannot but love her and submit his intellect to her doctrine and his heart to her precepts, and thus remain all his lifetime faithful to her.
After this proof from History that the Catholic Religion is Divine, the Catechism proper commences, and teaches us that we must submit to its doctrine; namely, that we must, 1. Believe what the Church teaches; 2. That we must also practise, that is, do the will of God; and 3. That we can neither believe nor do the will of God without His grace, which we receive by means of the Sacraments and of Prayer."
A Full Catechism of the Catholic Religion from 1889
It is interesting that the proof of the Divinity of the Roman Catholic Church should be determined from history books rather than God's book. If I were to fall for the "older is truer" idea, I think I would convert to Judaism.