That’s a good question. It’s not a matter of what “goes into” Tradition, but what was there from the beginning.
"The Church’s Magisterium exercises the authority it holds from Christ to the fullest extent when it defines dogmas, that is, when it proposes truths contained in divine Revelation." (CCC 88)
“And [Holy] Tradition transmits in its entirety the Word of God which as been entrusted to the apostles by Christ the Lord and the Holy Spirit. It transmits it to the successors of the apostles so that, enlightened by the Spirit of Truth, they may faithfully preserve, expound, and spread it abroad by their preaching.”
Tradition is divine revelation handed down by Christ, entrusted to the apostles and passed on to their successors by the Holy Spirit through the Magisterium of the Church. "The apostles entrusted the “Sacred Deposit” of the faith, contained in Sacred Scripture and Tradition, to the whole of the Church. “By adhering to [this heritage] the entire holy people, united to its pastors, remains always faithful to the teaching of the apostles, to the brotherhood, to the breaking of bread and prayers. So, in maintaining, practicing and professing the faith that has been handed on, there should be a remarkable harmony between the bishops and the faithful.” (CCC 84)
In the early Church, while the apostles were still alive, it would be easy to verify if a teaching were apostolic or not. Those who received apostolic teaching in turn would pass it on to others (1 Cor. 23, 1 Tim 6:20, 2 Tim. 1:-2). Something taught in all the churches and traceable to the apostles would be apostolic Tradition. In the early centuries of the Church, major heresies usually required councils to clearly define a particular teaching, not verify whether it was apostolic or not, and in that show the error of the particular heresy. Ecumenical councils had to be approved by the pope before they became binding on the Church, because only with the approval of the pope would they be considered infallible. It’s pretty remarkable at how quickly people were in the early Church were to pick up on errors, which indicates Tradition was widely known and recognized.