I have long believed that the Apostles jumped the gun by choosing Mathias as the replacement for Judas. I do believe that the Lord intended Paul to be the replacement. I wonder, too, if it is Paul’s name that will be on one of the twelve foundation stones of the city, rather than Mathias’s.
Apostleship is a spiritual gift only given by God.
The other 11 Apostles taking a vote, then praying to God to choose either one person or another to be manifest by their casting lots was simply praying to God to bless their idolatry.
Paul was the 12th Apostle, the Apostle to the Gentiles.
It might also be noted that even Paul didn’t always grasp His appointment. As a Pharisee, he frequently believed his charge was to return to Jerusalem and witness to Israel. As he proceeded by his volition, he frequently found himself redirected by Divine Providence back towards Rome.
God doesn’t need us acting independently of His Will to accomplish His Plan. By remaining in fellowship with Him, His Plan works beautifully.