Doesn’t the mass provide enough proof?
It is not like studying an extinct organism, or an archaeologist digging up the remains of a forgotten civilisation. The flow is held in living memories, the remembrance goes back in a living chain.
At every service there are present elderly people who, 50 or 60 years ago heard certain words spoken by, or in the presence of, men old enough to be their grandparents; there are young people who, it may be, will repeat them in the hearing of their grandchildren. And so the endless chain goes on. For 20 centuries there has not been one single week in which this act of remembrance was not made, one generation reminding another:
The Lord Jesus, on the night of his arrest, took bread, and after giving thanks to God, broke it and said: ‘This is my body, which is for you; do this as a memorial of me.’ In the same way he took the cup after supper and said, ‘This cup is the new covenant sealed with my blood. Whenever you drink it, do this as a memorial of me.’
Or words such as these.
One of the best illustrations of this continuity of memory within the Church for me is that around and about 200 AD there died at Lyon in France the Bishop of that city, Irenaeus by name, one of the outstanding Christian leaders of his time. It happens that a letter of his has come down to us, addressed to an old fellow student named Florinus from whom he had been seperated for many years. The letter brings up reminiscences of their student days together at the city of Smyrna in Asia Minor. In particular he recalls how they used to attend lectures by Polycarp, bishop of Smyrna, who died about 155 AD at the age of at least 86. He must have been getting on in years when Irenaeus and Florinus heard him. Irenaeus reminds his old companion- and there would have been no point in it if Florinus could not confirm his recollections- how Polycarp used to tell them stories about ‘John, the disciple of the Lord’, whom he had known personally many years before. Iraneaus, then, in France shortly before 200 AD was able to recall at only one remove, a man who had known Jesus intimately. When the Bishop of Lyons brooke bread with his little congregation as a memorial of the death of Jesus, he was not thinking of something he had found (where Kipling’s Tomlinson found his God) ‘in a printed book’, but of something that he had been told by his old teacher, whose friend had been there and knew. That is what the memory of the Church is like. A corporate memory handed down from generation to generation become what we call a tradition.
Our knowledge of about the origins of the church and about its Founder, rests primarily on a living tradition, which had its beginnings in the actual memories of those who had witnessed the events and had personal dealings with the principle Actor in them.
(Hey, next time I am up late studying and wired on caffeine, I might just try it! 
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