Why did Paul wait a week to teach the Gentiles?

Answer:

"But going on from Perga, they arrived at Pisidian Antioch, and on the Sabbath day they went into the synagogue and sat down. After the reading of the Law and the Prophets the  synagogue officials sent to them, saying, 'Brethren, if you have any word of exhortation for the people, say it.' Paul stood up, and motioning with his hand said, "Men of Israel, and you who fear God, listen: ...'" (Acts 13:14-16).

When Paul and his companions first arrived in Pisidian Antioch, there was no existing church. Paul had come to convert people to Christianity and establish a church. As was his custom, he started by going to the local Jewish synagogue. Here would be people who knew about God and the Law. His initial speech was well received.

"As Paul and Barnabas were going out, the people kept begging that these things might be spoken to them the next Sabbath. Now when the meeting of the synagogue had broken up, many of the Jews and of the God-fearing proselytes followed Paul and Barnabas, who, speaking to them, were urging them to continue in the grace of God. The next Sabbath nearly the whole city assembled to hear the word of the Lord. But when the Jews saw the crowds, they were filled with jealousy and began contradicting the things spoken by Paul, and were blaspheming. Paul and Barnabas spoke out boldly and said, 'It was necessary that the word of God be spoken to you first; since you repudiate it and judge yourselves unworthy of eternal life, behold, we are turning to the Gentiles. For so the Lord has commanded us, 'I have placed you as a light for the Gentiles, that you may bring salvation ot the end of the Earth.' When the Gentiles heard this, they began rejoicing and glorifying the word of the Lord; and as many as had been appointed to eternal life believed. And the word of the Lord was being spread through the whole region" (Acts 13:42-49).

Paul noted that it was necessary for him to attempt to teach the Jews first. "For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek" (Romans 1:16). This is the order in which God wanted His message taught. Once the Jews showed that they did not want the Gospel on the following Sabbath, Paul moved on to the Greeks. There is nothing in the text that indicates that he waited a week to teach the Gentiles. The only week's delay was between the first and second Sabbaths, to wait for the next gathering of the Jews. However, word had gotten out about Paul and what he was teaching because the second meeting drew nearly the whole city to hear him. The Jews rejected Paul, more for his popularity than for his message.

He began teaching the Gentiles, and this led to the establishment of a church in that town.