Did Paul expect the Rapture to happen while he was still alive?
Yes. Paul was already waiting for the coming of the Lord Jesus Christ, which is the Rapture, and he honestly thought it would take place in his lifetime. He had no idea that God would wait almost two thousand years.
Les teaches that Paul, writing to the Corinthians, was waiting for the coming of the Lord Jesus Christ—the Rapture. Paul honestly thought it would take place in his lifetime and had no idea God would wait almost 2,000 years. Les connects this to Paul's assurance that the Corinthians would be confirmed to the end and blameless in the day of the Lord Jesus Christ, since they were already under the blood and forgiven by the grace of God.
1 Corinthians 1:7
So that ye come behind in no gift; waiting for the coming of our Lord Jesus Christ: