score:3
I don't believe that your source actually describes total depravity as Calvin intended it. What is described here has never been at odds with Catholic teaching, and thus would never have been condemned as heresy. The weakened version of TD, that original sin "affects the whole person," has been known since the beginning of the Church. Even before that the Jews knew it and wrote psalms about it. As here defined, NigelJ's comment is correct. The Epistles of Paul would probably be the first Church document to support and mention the doctrine.
As stated by Calvin himself, the doctrine is something different. In this article on the topic, Tim Staples quotes Calvin's The Institutes of the Christian Religion as saying: βThe will is so utterly vitiated and corrupted in every part as to produce nothing but evilβ (Institutes, bk. II, ch. II, para. 26).
This is obviously at odds with the notion that "[y]ou might think of an archfiend of history such as Adolf Hitler and say there was absolutely no redeeming virtue in the man, but I suspect that he had some affection for his mother." No. If man's will is truly so utterly vitiated as to produce nothing but evil, then no. Hitler could not have had affection for his mother, because that is clearly not evil.
Hence, I would have to conclude that there are two answers to your question. When speaking of Total Depravity as defined by Calvin himself, The Institutes is the first example we have of it. Although, Luther might have been an slightly earlier example, without having called the doctrine by its formal name. The comment on the answer in that last link also mentions the Catholic Church's first formal denunciation of the doctrine, from Trent "If any one saith, that all works done before Justification, in whatsoever way they be done, are truly sins, or merit the hatred of God; or that the more earnestly one strives to dispose himself for grace, the more grievously he sins: let him be anathema." However, when speaking of Total Depravity according to the typical understanding of the modern Reformed Tradition, the idea is biblical and Catholic, so the bible would be the first document to mention it, because they idea is merely that men are depraved due to original sin, and not totally depraved, unable to will any good on their own.