You seem to be saying that Acts 20:7 shows that the disciples kept the first day of the week but I would like you to explain why in Acts 13:42-44; Acts 17:1-4; and Acts 18:1-4 that the Apostle Paul, along with the Jews and Gentiles, observed the Sabbath day more often than the first day of the week, which is recorded once in Acts 20:7.
Now my concerned is not Paul preaching to the Jews on the Sabbath day, because as you said they can observe it if they want, but the Gentiles are not obliged to observe it. So why didn't the Gentiles in these three chapters just tell Paul, since he was with them for more than two weeks, "preach to us on Sunday because that is our day."
When searching the Scriptures, it is important to note who are the participants before deciding this is an example that we are to follow. For instance, the Bible mentions several of the shady activities of Judas Iscariot. But we would not appeal to what Judas did as an example for what we should do because we read, "Jesus answered, "It is he to whom I shall give a piece of bread when I have dipped it." And having dipped the bread, He gave it to Judas Iscariot, the son of Simon. Now after the piece of bread, Satan entered him. Then Jesus said to him, "What you do, do quickly"" (John 13:26-27). We follow examples because the person is following Christ. "Imitate me, just as I also imitate Christ" (I Corinthians 11:1).
"But when they departed from Perga, they came to Antioch in Pisidia, and went into the synagogue on the Sabbath day and sat down. And after the reading of the Law and the Prophets, the rulers of the synagogue sent to them, saying, "Men and brethren, if you have any word of exhortation for the people, say on." Then Paul stood up, and motioning with his hand said, "Men of Israel, and you who fear God, listen: ... So when the Jews went out of the synagogue, the Gentiles begged that these words might be preached to them the next Sabbath. Now when the congregation had broken up, many of the Jews and devout proselytes followed Paul and Barnabas, who, speaking to them, persuaded them to continue in the grace of God. On the next Sabbath almost the whole city came together to hear the word of God. But when the Jews saw the multitudes, they were filled with envy; and contradicting and blaspheming, they opposed the things spoken by Paul. Then Paul and Barnabas grew bold and said, "It was necessary that the word of God should be spoken to you first; but since you reject it, and judge yourselves unworthy of everlasting life, behold, we turn to the Gentiles" (Acts 13:13-16, 42-46).
In Acts 13, Paul was at the Jewish synagogue teaching people about the Christ. The day Jews gathered at the synagogue was the Sabbath day, thus it makes perfect sense that the opportunity to teach about Jesus was on that day for that audience. Notice that Paul's audience was composed of Jews, devout proselytes, and Gentiles. Therefore we learn that some Gentiles came to the Jewish synagogues -- some because they had converted and others, like Cornelius in Acts 10, because they were interested in God though they had not converted. It was these Gentiles who asked Paul to speak again at the next assembly, which would be on the next Sabbath day because we must remember that Paul was preaching at this time in a Jewish synagogue. Some there did talk to Paul and Barnabas during the week and were converted. Word went out and on the next Sabbath, the whole city came to the synagogue to hear Paul, which caused the Jews to become jealous and oppose Paul. It is then that Paul stated he would continue his work among the Gentiles. Thereafter you do not see mention of what day of the week these Gentiles met.
Thus you are attempting to apply the meeting day of Jews, proselytes, Gentiles interested in the Old Testament (in other words, non-Christians) to the meeting day of Christians. That is not a proper application of the Scriptures.
"Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where there was a synagogue of the Jews. Then Paul, as his custom was, went in to them, and for three Sabbaths reasoned with them from the Scriptures, explaining and demonstrating that the Christ had to suffer and rise again from the dead, and saying, "This Jesus whom I preach to you is the Christ." And some of them were persuaded; and a great multitude of the devout Greeks, and not a few of the leading women, joined Paul and Silas. But the Jews who were not persuaded, becoming envious, took some of the evil men from the marketplace, and gathering a mob, set all the city in an uproar and attacked the house of Jason, and sought to bring them out to the people" (Acts 17:1-5).
Once again Paul went to a Jewish synagogue to teach on the day the Jews assembled, the Sabbath day. He did so for three weeks in a row. As a result, he persuaded some of the Jews and a great number of the devote Gentiles (Gentiles assembling with the Jews), along with some leading women of the city. This again tells us that Paul went and taught among the Jews and those sympathetic to the Jews on the days they assembled. It does not tell us what day those who became Christians, as a result of Paul's teaching, assembled.
Acts 18 is like the previous ones. "And he reasoned in the synagogue every Sabbath, and persuaded both Jews and Greeks" (Acts 18:4). It tells us that Paul taught those who were Jews and those who assembled with the Jews in the Jewish synagogues on the Sabbath day. He was able to persuade some of these non-Christian people at the assemblies to become Christians. The passages tell us where and when Paul taught non-Christians. It does not tell us when those who became Christians met.
But Acts 20:7 is different. "Now on the first day of the week, when the disciples came together to break bread, Paul, ready to depart the next day, spoke to them and continued his message until midnight" (Acts 20:7). This was a gathering of Christians (not Jews or Jewish sympathizers). It tells us that they met on the first day of the week. It also tells us why they met on this particular day of the week, this is when disciples came together to partake of the Lord's Supper (an act of worship).
I can use Acts 13, 17, and 18 to show that it is proper to teach the gospel among non-Christians when opportunities arise to speak at their gathers. There is no restriction that preaching can only take place on one day of the week. But if I want to know when Christians met to worship, then I must turn to the example of when Christians actually met and it mentions when they did so.