Summary: We may not all be Apostles, but we all have a role to play.
THE APOSTOLIC FOUNDATION OF THE CHURCH
When Jesus appeared to “the eleven” and the rest of the Upper Room assembly after His resurrection, He demonstrated the need for His death and resurrection from the Scriptures of the Old Testament, viz. “the Law of Moses and the Prophets and the Psalms” (Luke 24:44-45).
I wonder which Psalms Jesus mentioned? There are so many which speak more-or-less directly about His Messianic work. One strand of teaching from the Psalms was particularly in Peter's mind when he suggested that the now dead traitor Judas Iscariot must needs be replaced (Acts 1:16).
In Psalm 41:9 David says, “Even my own familiar friend in whom I trusted, who ate my bread, has lifted up his heel against me.”
In John 6:70 Jesus had said, “Did not I choose you twelve, and one of you is a devil?”
When the assembly met again after the ascension, Peter said of Judas, “he was numbered with us and obtained a part in this ministry” (Acts 1:17).
Numbered with whom? With the twelve, who had now become the eleven. They were appointed by Jesus, and named “apostles” by Him, and their names are given in the Gospels (e.g. Luke 6:12-16). In Acts 1:2 the eleven are entitled, “the apostles whom He had chosen,” and it was to the Lord's choice that the church submitted themselves for a replacement for Judas (Acts 1:24).
In Acts 1:20 Peter quoted two Messianic Psalms to explain the need to replace Judas.
Psalm 69 is quoted in reference to Jesus on several occasions.
Psalm 109 is a prolonged plea against the enemies of Jesus.
One of the qualifications of Judas' replacement was that he should be one of those who had accompanied the disciples from the very beginning of Jesus' ministry right through to the ascension. He was also to be a witness with them to the resurrection, so it was imperative that he should have seen the risen Lord.
The church chose two candidates. They prayed for the Lord's choice between them, and drew lots. Remember that the Holy Spirit had not yet fallen upon them: this is the last time in the Scriptural record that this Old Testament device was used. The lot fell on Matthias, and he was numbered with the eleven.
Some people have argued that the apostles were wrong in appointing Matthias. After all, we never hear of him again in the canon of Scripture. I think this may be true of other apostles, too, so that argument is moot.