You assume "wait" meant "do nothing".
The Lord simply commanded them
not to depart Jerusalem but "wait for the Promise of the Father, “which,”
He said, “you have heard from Me; for John truly baptized with water, but you shall be baptized with the Holy Spirit not many days from now.”
After they chose Matthias they were baptized with the Holy Spirit. From then on, the record of Acts and of Paul contain "the twelve" which could mean nothing other than the twelve apostles who came out of the upper room. This fulfilled the scriptures Peter noted and their number functioned to confirm that the proclamation (that Jesus was, in fact, the Son of God) was legally binding and true by Jewish standards.
There is so much resistance to this because of doctrinal tradition and, perhaps, because of our bias toward celebrity. Sure Paul was important, but he was not one the the twelve. Unlike us, God is no respecter of persons. I also think there is a bit of "God works in mysterious ways" mentality that gets in the way of our understanding. So we are apt to accept church doctrine without searching it out for ourselves. God is actually our Father, not an author of confusion, and He tells us plainly in scripture what is true. Certainly, "
It is the glory of God to conceal a matter and the glory of kings to search it out" but our diligent search comes with a promise: God's reward.
Good Night Friends,
Aaron56