How do we explain Paul's encounters with disciples of Jesus in light of the Great Commission?

The following passage relates the "Great Commission" that Jesus gave to 11 disciples: https://www.biblegateway.com/passage/?search=Matthew%2028:16-20 But Paul, a man who never met Jesus during his life, seems to have taken up the mantle all by himself: > 13I am talking to you Gentiles. Inasmuch as I am the apostle to the > Gentiles, I take pride in my ministry 14in the hope that I may somehow > arouse my own people to envy and save some of them. 15For if their > rejection brought reconciliation to the world, what will their > acceptance be but life from the dead? 16If the part of the dough > offered as firstfruits is holy, then the whole batch is holy; if the > root is holy, so are the branches. In Acts 10, Cornelius comes to Peter, and he is already following God. And then Peter baptizes him. OK, but that's hardly "going out and making disciples of all the nations". In Acts 15, Peter seems to recall that he (alone?) was supposed to be apostle to the Gentiles. He concludes by saying: > 19“It is my judgment, therefore, that we should not make it difficult > for the Gentiles who are turning to God. 20Instead we should write to > them, telling them to abstain from food polluted by idols, from sexual > immorality, from the meat of strangled animals and from blood. 21For > the law of Moses has been preached in every city from the earliest > times and is read in the synagogues on every Sabbath.” So it was only then decided what the gentiles should do. Which means that this whole time, it was mostly Paul converting the gentiles. What happened to the 11 apostles? Where are their epistles? Who were they converting among the gentiles? According to the Great Commission, they should be baptizing them in the name of the trinity. Why was Paul given the job? Is part of the explanation that the Great Commission was added later to the Gospel of Matthew?