Why did God turn to the Gentiles instead of the Jews?
At that particular time, the Jews had to recognize that Jesus was the Christ, and only Jesus. But the vast majority rejected Him as Messiah and Redeemer; they let the ball drop. Therefore God went to the Gentile without them.
Les explains that Peter is dealing with the Jew at this particular time, and they had to recognize that Jesus was the Christ, and only Jesus. The verse is narrow—there is no other name under heaven given among men whereby we must be saved. Many Jews early on did embrace Christ as their Messiah and Redeemer, as archaeology is proving, but the vast majority rejected it. Because they let the ball drop, God went to the Gentile without them. However, the context notes we're not there yet; Peter is still dealing with the covenant people.