St. Alphonsus gives beautiful classical traditional Catholic explanation of the proofs of faith I had not read before. I found it while looking for a quote of his Stubborn mentioned. It is after a person knows and has been informed of these proofs of faith along with the preaching of faith and then stubbornly refuses to hear and enter the Church (like for e.g. in Mat 18:17), such a person cannot be saved (cf. Holy Office Letter). Not someone who has never heard the Church and can't hear Her preach. Here is the passage. Our Lord also refers to this traditional principle in the Gospel of Saint John when He says: "If I had not done among them the works that no other man hath done, they would not have sin; but now they have both seen and hated both Me and My Father."(John 15:24). It is that hatred and rejection of Jesus Christ that is the mortal sin.

From: https://www.ecatholic2000.com/liguori/school/perfect.shtml The School of
Christian Perfection


"PROOFS OF FAITH
In the first place, the truth of our holy faith is loudly proclaimed by the prophecies of Holy Scripture. These prophecies were uttered hundreds of years ago, and in later years fulfilled to the letter. Thus, for example, the death of our Saviour was foretold by several prophets and the time and circuмstances accompanying it minutely described. It was prophesied that the Jєωs, in punishment for the deicide, would be driven from the temple and the holy land, and hardened and obstinate in sin would be dispersed throughout the world; this prophecy, we know, was literally fulfilled. It was prophesied that after the death of Christ the veneration of heathen deities would give way to the worship of the true God. The event has verified the prediction, for the Apostles of Our Lord, in spite of the innumerable obstacles thrown in their way and armed with no weapons save the cross of Christ, have conquered the world and brought it a captive to faith in the living God.
In the second place, the truth of our holy faith is evident from the miracles which were wrought by our Lord, by His Apostles and the Saints of the Catholic Church as a sanction of her holy teaching. Miracles are beyond the powers of nature. They can happen only by the power of God, to whom all creation is subject. Accordingly, if a religion has real miracles to show in confirmation of her doctrine, that religion must be divine, for it is impossible for God to sanction and promote a false religion by the performance of genuine miracles.
Can the Jєωs, the heathens, the Mohammedans or the heretics point to a single miracle wrought in favor of their religious tenets? They have no doubt made efforts in the past to deceive the people by trickery and the seemingly miraculous; the deception was soon discovered. But the miracles which God has worked through His servants in every age of the Catholic Church are simply innumerable. In the Catholic Church alone have the words of our Blessed Lord been fulfilled: “Amen, amen I say to you, he that believeth in me, the works that I do he also shall do; and greater than these shall he do.” (John 14:12).
Without doubt, in the early days of the Church miracles were more numerous than they are today, since they were necessary for the spread of the Faith. But still they have never been wanting in any age, and they have constantly aided in the conversion of heathen and infidel nations. Numberless miracles were performed, for example, by a St. Francis Xavier, a St. Louis Bertrand, and other holy missionaries in India. Were one to call into question the extraordinary facts recorded in the annals of Church history and in the lives of the Saints, I would simply ask him: By what right do you refuse to believe such men as St. Basil, St. Jerome, St. Gregory and others when you willingly accept what a Tacitus, a Suetonius, or a Pliny has said?
Moreover, God has been pleased to allow certain miracles to go on uninterruptedly in the Church as a continual reproach to the unbelief of the wicked. Recall to mind the famous miracle of the liquefaction of the blood of St. Januarius at Naples. This blood, which usually is found in a hardened, coagulated condition, liquifies several times a year when brought near the head of the Saint. This has been attested by thousands of eyewitnesses. Infidels have tried in vain to find natural explanations for the phenomenon; but the miracle continues to baffle their efforts and to humble their pride.
A third proof for the truth of our holy faith is furnished by the courage and constancy of the martyrs, and this proof is more convincing even than that of miracles. Fifteen Roman emperors in succession used every means in their power to destroy the Christian faith from the face of the earth. Under the reign of Diocletian, who inaugurated the ninth persecution, 17,000 Christians were executed within a single month, not to speak of the thousands who were banished from the country.
According to the account of Genebrard, 11,000,000 martyrs were put to death during the ten great persecutions. If these were gathered within the space of one year, there would be 30,000 martyrs for each day. Now in spite of the fact that these confessors of Christ were subjected to every imaginable torture, such as the tearing of the flesh with iron hooks, roasting their bodies on a gridiron, and burning them with lighted torches, the number of those who were willing and anxious to die for their holy faith was never diminished but seemed always on the increase.
Tiberius, the governor of Palestine, wrote to the Emperor Trajan that there were so many Christians who desired to die as martyrs that it was impossible to execute them all. Hereupon Trajan published an edict in which he commanded the Christians to be left in peace for the future. Now I ask: If the Faith of these valiant martyrs, which is the same that our Holy Church professes today, were not the True Faith of Christ, and had not God assisted them to witness to that Faith with their very blood, would they ever have been able to endure those frightful torments and to deliver themselves up freely and joyfully to a cruel death? Have there been any martyrs in the sects that fell away from the Catholic Church? Have they perhaps a St. Lawrence who offered his roasted limbs to the cruel tyrant for a banquet? Have they perhaps a St. Marcellus or Marcellinus whose feet were pierced with nails; when urged to free themselves from torture by renouncing their holy faith, they replied: “You speak of torments, but we have never experienced a greater joy than at present when we suffer for the love of Jesus Christ.” Have they perhaps a St. Processus or a St. Martinian whose bodies were burned with red-hot plates and torn with iron hooks? In the midst of their sufferings they sang hymns of praise to God and yearned to die for Christ.
Add to these martyrs of the first ages the numberless men and women of later days who suffered the most excruciating torments that human cruelty could devise and gave their life for their holy faith. How many died during the 16th century in Japan alone? We select the following facts from the list of cruelties perpetrated during the savage persecution that raged in Japan. A woman named Monica ardently desired to die as a martyr for Christ. To render herself proof against weakness when suffering from the executioners, she practiced beforehand what she thought she might have to endure. One day she grasped a red-hot iron in her hand. Her sister cried out: “O Monica, what are you doing?” “I am preparing myself,” she replied, “for a martyr’s death. I have already resisted the cravings of hunger and I have overcome that danger. Now I am trying fire so as to be able to endure it when subjected to its torture.”
Another woman said to her companions: “I am firmly resolved to give my life for my holy faith. But if at the approach of death you see me tremble, I beg you to drag me by main force to the executioners in order that I may share your crown.” A boy named Anthony replied to his parents, who begged him with tears to renounce his faith: “Cease torturing me with your words and complaints; I am resolved once and for all to die for the love of Jesus Christ.” And when, like his Divine Master, he hung on the cross, he intoned the words of the 112th Psalm: “Praise the Lord, ye children.” He sang it as far as the “Glory be to the Father,” when he expired and went to complete the hymn of praise in Heaven. Another boy said to his father: “I will rather suffer death at the hands of the executioners or at your own hands than refuse obedience to God; I will not cast myself into Hell for the sake of pleasing any man.” A servant spoke thus to his master: “I know what Heaven is worth; and since a martyr’s death is the shortest road that leads me thither I choose it with joy, and I esteem my earthly life as little as the dust beneath my feet.”
A woman by the name of Ursula had seen her husband and her two children put to death for their faith; with tears in her eyes she exclaimed: “I thank Thee, my God, that Thou hast deemed me worthy to make this offering; grant me also the crown which now adorns my loved ones. All I have left is the little child I carry in my arms. I gladly offer it with myself; graciously accept this last offering which I make to Thee.” She then pressed the child to her heart, and one stroke of the sword beheaded the mother and the daughter.
Another mother called out continually to her son who, like herself, was fastened to a cross: “Courage, my son, courage! We are on the way to Heaven. Continue to call on Jesus and Mary.” A nobleman named Simon said: “What a happiness for me to be permitted to die for my Redeemer! How have I ever deserved so great a favor?” A little blind girl of eight years clung closely to her mother so as to be able to die with her on the funeral pyre. A boy of five years of age was roused out of sleep to be led off to a cruel death. Without betraying the least alarm he put on his best clothes and was then carried off to the place of execution. On their arrival the little lad himself offered his neck to the executioner. The latter was so moved at the sight of this tender child that he was unable to perform his duty. Another had to take his place, and it was only after several strokes of the sword that an end was put to the child’s life. All these facts were attested by declared enemies of our Holy Church.
Once more the proof of our holy faith becomes evident when we consider that from the time of the Apostles down to our own days our Faith has continued unaltered. The Apostles and their successors were careful to preserve the doctrine of our Divine Redeemer in its primitive purity and integrity. Christ Himself imposed upon them this sacred duty when He said: “Going therefore, teach ye all nations; teach them to observe all things whatsoever I have commanded you.” (Matt. 28:19–20). Therefore St. John exhorts the faithful: “Let that which you have heard from the beginning abide in you.” (1 John 2:24).
The Apostle Jude writes: “I beseech you, dearly beloved, to contend earnestly for the faith once delivered to the saints.” (Jude 3).
Similar are the exhortations of the Apostle St. Paul when writing to the Ephesians: “I beseech you, brethren, that you be careful to keep the unity of the Spirit in the bond of peace” (Eph. 4:3), and to the Corinthians: “Let there be no schisms among you; but be perfect in the same mind and in the same judgment.” (1 Cor. 1:10).
These admonitions of the Apostle have always been strictly adhered to by the pastors of the Church, for, in the words of St. Augustine, “What they found in the Church they have preserved, and what their fathers handed down to them they in turn left as a precious legacy to their sons.” Accordingly, the Catholic Church has remained the same in all ages and in all climes. The doctrines she teaches today are the same that were taught and believed in the first ages of the Church. The sects, on the contrary, that have separated from the Catholic Church, have not remained unchanged in the doctrines which they propound. If you desire an illustration of this, read the History of the Variations by the famous Bishop Bossuet. There you will find an authentic record of the everchanging tenets of the Protestant denominations. The pride that caused the founders of these sects to refuse obedience to the true Church of Christ has led their followers in turn to refuse obedience to them, and thus countless new doctrines and new religions have sprung into existence. It is of immense advantage for us who are faithful adherents of the true Church of God to read and ponder the accounts that are found in the history of heresies. Such a reflection is calculated to bring into a most favorable light our own True Faith that, like our Saviour Himself, is “yesterday, and today, and the same forever.” (Heb. 13:8). It will foster in us a spirit of loyal submission to our Holy Church, and a deep sense of gratitude to God for the inestimable gift of the True Faith.