Did Paul go to the Gentiles with the message that Christ died for the sins of the world right after his conversion?
No. Right after his conversion and baptism, Paul did not go to Gentiles with the message that Christ died for the sins of the world. Instead, he entered the synagogue and taught that Jesus is the Christ, the Son of the Living God.
Les explains that after Paul was saved by grace on the road to Damascus, he did not yet understand that Christ died for him. Once Paul received food, regained his sight, and was baptized, he went directly to the synagogue, not out into the marketplace to proclaim to Gentiles that Christ died for the sins of the world. There he taught that Jesus is the Christ, the Son of the Living God. Les says he will point this out when they get into the book of Acts.