What needed to happen before the believers were ready to take the Gospel to the Gentiles?

Before the Gospel went to the Gentiles, God saved Saul and sent Peter to Cornelius. Saul had already come back from his three years of learning and the revelation of the mysteries. Only then were the Jewish believers ready to speak to Greeks and preach the Lord Jesus.

Les explains that God started the ball rolling toward the Gentile world when He saved Saul, and then speeded it up when He sent Peter up to Cornelius. But Saul had already come back from his three years of learning and the revelation of the mysteries. At that point, they were ready to get down to brass tacks and get the Gospel out to the Gentiles. This was a complete change in venue and modus operandi, because the Jewish believers had been preaching to Jews only. Now they began to speak to Greeks and preach the Lord Jesus, and the hand of the Lord was with them. A great number believed and turned unto the Lord.

Why were the believers ready to start preaching to Gentiles at this point in Acts?

God had already begun moving toward Gentiles: He saved Saul, then sent Peter to Cornelius, and now Saul had returned after three years of learning and the revelation of the mysteries. With God's hand with them, Jewish believers who formerly preached only to Jews began speaking to Greeks.