What about Paul?
Paul was an apostle, but he was not one of the Twelve. Paul—also known as Saul—is easily one of the most widely-known biblical figures (he wrote most of the New Testament books, after all), and he often appears on lists of the most influential people who have ever lived. Paul did more to help spread the gospel throughout the world than anyone else in the early church.

But he wasn’t one of the Twelve, and he probably never encountered Jesus during his earthly ministry. Before his dramatic conversion, Paul was a member of the Pharisees—a group of religious elites who opposed Jesus and persecuted his followers. Acts even records that Paul watched and approved while people stoned the first Christian martyr (Stephen) to death (Acts 8:1).
On the road to Damascus, where Paul intended to arrest Christians, Jesus appeared to him, asking: “Saul, Saul, why do you persecute me?” (Acts 9:4) Then the Lord told Paul, “Now get up and go into the city, and you will be told what you must do” (Acts 9:6). Paul was struck blind, and Jesus used a man named Ananias to restore his sight in Jerusalem.
From that point forward, Paul became the apostle to the Gentiles (Romans 1:13) and claimed Jesus had specifically called him to reach non-Jewish communities (Acts 22:21).
Since Jesus called Paul but didn’t call Matthias, some have argued that Paul was intended to be the apostle to replace Judas Iscariot. (Which would be poetic: Satan turned one of Jesus’ closest followers against him, but Jesus turned one of the strongest adversaries of the Church into one of her strongest advocates.)