This is actually a very interesting question, which we could rephrase as "When did Tradition [in the Catholic/Orthodox sense] became a Dogma?"
Every historical declaration of dogma/doctrine by the Catholic Church is recorded in the Enchiridion (usually cited as DS; English version online here). Therefore, we can search that document for "tradition". As can be seen from the quotes and the heading in the DS document however, this concept is in the beginning often found tied with that of "Infallibility of the Roman Pontiff". In effect, under the view of the Catholic Church these are inseparable because, as expressed in Lumen Gentium:
In virtue of his office, that is as Vicar of Christ and pastor of the whole Church, the Roman Pontiff has full, supreme and universal power over the Church. And he is always free to exercise this power. The order of bishops, which succeeds to the college of apostles and gives this apostolic body continued existence, is also the subject of supreme and full power over the universal Church, provided we understand this body together with its head the Roman Pontiff and never without this head. This power can be exercised only with the consent of the Roman Pontiff. For our Lord placed Simon alone as the rock and the bearer of the keys of the Church, and made him shepherd of the whole flock;(Jn 21,15f.) it is evident, however, that the power of binding and loosing, which was given to Peter,(Mt 16,19) was granted also to the college of apostles, joined with their head.( Mt 18,18; 28,16-20)
So, if we look for these concepts, we can find the following, in chronological order:
417 AD: Pope (saint) Innocent I, in the letter In requirendis, writes:
In seeking the things of God . . . preserving the examples of ancient tradition . . . you have strengthened the vigor of your religion . . . with true reason, for you have confirmed that reference must be made to our judgment, realizing what is due the Apostolic See, since all of us placed in this position desire to follow the Apostle, from whom the episcopate itself and all the authority of this name have emerged. Following him we know how to condemn evils just as (well as how) to approve praiseworthy things. Take this as an example, guarding with your sacerdotal office the practices of the fathers you resolve that (they) must not be trampled upon, because they made their decisions not by human, but by divine judgment, ...
418 AD: The letter Quamvis Patrum traditio by Pope saint Zosimus:
Although the tradition of the Fathers has attributed such great authority to the Apostolic See that no one would dare to disagree wholly with its judgment, and it has always preserved this judgment by canons and rules, and current ecclesiastical discipline up to this time by its laws pays the reverence which is due to the name of PETER, from whom it has itself descended . . . ; since therefore PETER the head is of such great authority and he has confirmed the subsequent endeavors of all our ancestors, so that the Roman Church is fortified . . . by human as well as by divine laws, and it does not escape you that we rule its place and also hold power of the name itself, nevertheless you know, dearest brethren, and as priests you ought to know, although we have such great authority that no one can dare to retract from our decision, yet we have done nothing which we have not voluntarily referred to your notice by letters . . . not because we did not know what ought to be done, or would do anything which by going against the advantage of the Church, would be displeasing.
422 AD: Pope (saint) Boniface I also wrote a doctrinal document with these issues, but it is a bit too long to put here. See the DS website linked above. It has the same type of "indirect" claims.
433 AD: Pope (saint) Sixtus III says (in the Latin version, sorry):
De Dei autem Genetrice Virgine quemadmodum et sapimus et dicimus et de modo humanationis unigeniti Filii Dei necessariae, non additamenti causa, sed ad satisfactionem proprie desuper tam de divinis scripturis quam de traditione sanctorum patrum adsumentes habuimus, breviter dicimus, nihil omnino addentes fidei sanctorum patrum, quae in Nicaea exposita est.
The key is where he says (my translation) that the Truth about the human nature of Jesus through Virgin Mary, "has been received from old, both from the sacred Scriptures and the tradition of the Holy Fathers".
There are plenty of these - some might argue - "indirect" mentions. Yet, the issue seems to become clearer over time. One of the last examples is from Pope (saint) Simplicius, in 476 AD, and found under the heading of "The Unchangeableness of Christian Doctrine":
Those genuine and clear [truths] which flow from the very pure fountains of the Scriptures cannot be disturbed by any arguments of misty subtlety. For this same norm of apostolic doctrine endures in the successors of him upon whom the Lord imposed the care of the whole sheepfold [John 21:15 ff.], whom [He promised] He would not fail even to the end of the world [Matt. 28:20], against whom He promised that the gates of hell would never prevail, by whose judgment He testified that what was bound on earth could not be loosed in heaven [Matt. 16:18 ff.]. (6). . . Let whoever, as the Apostle proclaimed, attempts to disseminate something other, than what we have received, be anathema[ Gal. 1:8 f.]. Let no approach to your ears be thrown open to the pernicious plans of undermining, let no pledge of revising any of the old definitions be granted, because, as it must be repeated very often, what has deserved to be cut away with the sharp edge of the evangelical pruninghook by apostolic hands with the approval of the universal Church, cannot acquire the strength for a rebirth nor is it able to return to the fruitful shoot of the master's vine, because it is evident that it has been destined to eternal fire.
Yet, what seems to be the first direct treatment of this as doctrine (i.e. in the DS), occurs in the acts of the Council of Constantinople, in 553 AD. We read, under the heading of "Ecclesiastical Tradition" :
We confess that (we) hold and declare the faith given from the beginning by the great God and our Savior Jesus Christ to the Holy Apostles, and preached by them in the whole world; which the sacred Fathers both confessed and explained, and handed down to the holy churches, and especially [those Fathers] who assembled in the four sacred Synods, whom we follow and accept through all things and in all things . . . judging as at odds with piety all things, indeed, which are not in accord with what has been defined as right faith by the same four holy Councils, we condemn and anathematize them.
From all this, I conclude that, just as so many other dogmas, and without diminishing the value of such clarified truth (see below), the Church came to realise about the dogma of Tradition over several centuries, and was declared as such in 553 AD. Importantly, this does not mean that other Early Church Fathers did not write about it (even in dissimilar ways like Irenaeus or Augustine). It only means that it was not "entrenched" as doctrine until later.
I think it is worth adding here perhaps the clearest doctrinal declaration on the issue of the sources of Revealed Truth. It comes (perhaps unsurprisingly) from the fourth session (1546) of the Council of Trent. The entry in the DS is as follows:
The sacred and holy ecumenical and general Synod of Trent, lawfully assembled in the Holy Spirit, with the same three Legates of the Apostolic See presiding over it, keeping this constantly in view, that with the abolishing of errors, the purity itself of the Gospel is preserved in the Church, which promised before through the Prophets in the Holy Scriptures our Lord Jesus Christ the Son of God first promulgated with His own mouth, and then commanded "to be preached" by His apostles "to every creature" as the source of every saving truth and of instruction in morals [Matt. 28:19ff., Mark 16:15], and [the Synod] clearly perceiving that this truth and instruction are contained in the written books and in the unwritten traditions, which have been received by the apostles from the mouth of Christ Himself, or from the apostles themselves, at the dictation of the Holy Spirit, have come down even to us, transmitted as it were from hand to hand, [the Synod] following the examples of the orthodox Fathers, receives and holds in veneration with an equal affection of piety and reverence all the books both of the Old and of the New Testament, since one God is the author or both, and also the traditions themselves, those that appertain both to faith and to morals, as having been dictated either by Christ's own word of mouth, or by the Holy Spirit, and preserved in the Catholic Church by a continuous succession.
Having said this, the way you put the question is loaded, particularly knowing that you do not believe Tradition is a valid concept at all. Why is it loaded? Because for someone who does not believe in it, tradition became [wrongly] Tradition at a given time, because of non-supernatural inspired human decision. The answer to this perspective is then (if correct), the one given above. For someone who believe Tradition is Revealed Truth however, we know that the Catholic Church (Orthodox?) tells us that the establishment of a Dogma is not the creation of new truths, but the clarification of already Revealed Truths, made possible through the passage of time. Thus, in this sense, tradition never really became Tradition, since it always has been (as in the other answer).