Although there were certainly detractors (1 Corinthians 9:2), we can also demonstrate that Paul met the qualifications as set out by Luke and is a legitimate apostle of the Lord Jesus.
Acts 5:34-39
But a Pharisee in the council named Gamaliel, a teacher of the law held in honor by all the people, stood up and gave orders to put the men outside for a little while.
And he said to them, "Men of Israel, take care what you are about to do with these men.
For before these days Theudas rose up, claiming to be somebody, and a number of men, about four hundred, joined him. He was killed, and all who followed him were dispersed and came to nothing.
After him Judas the Galilean rose up in the days of the census and drew away some of the people after him. He too perished, and all who followed him were scattered.
So in the present case I tell you, keep away from these men and let them alone, for if this plan or this undertaking is of man, it will fail;
but if it is of God, you will not be able to overthrow them. You might even be found opposing God!"
Acts 7:58
And the witnesses laid down their garments at the feet of a young man named Saul.
Acts 21:17
When we[, Paul and Luke,] had come to Jerusalem, the brothers received us gladly.
Acts 22:3
"I am a Jew, born in Tarsus in Cilicia, but brought up in this city, educated at the feet of Gamaliel according to the strict manner of the law of our fathers, being zealous for God as all of you are this day."
Acts 26:4
"My manner of life from my youth, spent from the beginning among my own nation and in Jerusalem, is known by all the Jews."
Acts 26:13-18
"At midday, O king, I saw on the way a light from heaven, brighter than the sun, that shone around me and those who journeyed with me.
And when we had all fallen to the ground, I heard a voice saying to me in the Hebrew language, 'Saul, Saul, why are you persecuting me? It is hard for you to kick against the goads.'
And I said, 'Who are you, Lord?' And the Lord said, 'I am Jesus whom you are persecuting.
But rise and stand upon your feet, for I have appeared to you for this purpose, to appoint you as a servant and witness to the things in which you have seen me and to those in which I will appear to you,
delivering you from your people and from the Gentiles--to whom I am sending you
to open their eyes, so that they may turn from darkness to light and from the power of Satan to God, that they may receive forgiveness of sins and a place among those who are sanctified by faith in me.'"
In Acts 26 above, both "a light from heaven" and "I am Jesus" correspond to the other apostles witnessing His ascension into Heaven.
In the same way, "It is hard for you to kick against the goads," corresponds to the baptism of Jesus.
When Jesus was baptized by John "...and was praying, the heavens were opened, and the Holy Spirit descended on him in bodily form, like a dove; and a voice came from heaven, 'You are my beloved Son; with you I am well pleased.'" (Luke 3:21-22)
The baptism of Jesus was a time for God to bear witness to His Son.
The testimony of God goads people to believe in Jesus.
And just as in Mark 3:14, "And he appointed twelve (whom he also named apostles)," so here Paul is directly appointed by the Lord a servant and witness to the world.
1 Corinthians 15:1-3
Now I would remind you, brothers, of the gospel I preached to you, which you received, in which you stand,
and by which you are being saved, if you hold fast to the word I preached to you--unless you believed in vain.
For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures....
1 Corinthians 15:8
Last of all, as to one untimely born, he appeared also to me.
1 Corinthians 15:11
Whether then it was I or they, so we preach and so you believed.