Why couldn't Peter announce salvation for the whole human race through Christ's death, burial, and resurrection in Acts 10?
Peter could not announce it because God had not yet spoken or revealed that He would save the whole human race through Christ's shed blood, death, burial, and resurrection. That gospel was still hidden in God's mind, a secret kept since the world began, so Peter did not yet know it.
Les explains that everything concerning what we call the gospel was still hidden in the mind of God. No one can believe something God has never said; people believed only after He said it. God had not yet said He would save the whole human race based on Christ's shed blood, death, burial, and resurrection, and so Peter could not say it. Les then points to Romans 16:25, where Paul writes about the revelation of the mystery or secret kept secret since the world began. Paul was preaching something God had kept secret; Peter didn't know it because it hadn't been revealed yet.