I have several pages devoted to the Sunday Sabbath, but this question was direct. It seemed good to post my answer.
I can only say what the early Christians said. They said that the Jews, being fleshly, could only sanctify one day to the Lord. The Lord gave them such things as the Sabbath and sacrifices to help them keep their minds on him.
Now, though, we have entered the eighth day, the day of the new creation, and Christians, being spiritual, can live in the rest of Christ every day. We can sanctify every day to the Lord.
I think Hebrews 4 says this pretty clearly. Colossians 2 says the Sabbath was a shadow of things to come. I've had Seventh Day Adventists tell me that the Sabbath in Col. 2 is a reference to "high Sabbaths" that occur yearly during feasts. The problem with this is that the phrase "Feasts, new moons, and Sabbaths" is a pretty common Old Testament phrase for the yearly, monthly, and weekly special sacrifices (1 Chr. 23:31; 2 Chr. 2:4; 2 Chr. 8:13; 2 Chr. 31:3; Neh. 10:33; Ezek. 45:17; Hos. 2:11)
Paul, as familiar as he was with the Scriptures, had to have known that when he used the phrase.
It's always possible that meeting on the 1st day of the week developed later than apostolic times. (Meeting on the 1st day of the week is different than having a Sunday Sabbath.)
It's doubtful, though, for the following reasons:
Sabbatarians are correct that in the Scripture the apostles were gathering in the synagogues on the Sabbath. When does that leave them the opportunity to meet with the church?
The early Church argued that for them the Lord's Day, the first day of the week, was a day of rejoicing because it was the day on which Christ rose. It was not a new Sunday Sabbath. It was not a day of rest. It was a day of rejoicing.
All of that makes sense. Of course it was a day of rejoicing. Christ rose on that day. Why not meet on that day? The Jerusalem church would be trying to continue to meet with the Jews in the synagogue until they were thrown out, which is also what Paul did. So when would be a great time for the church to meet? The answer is the very next day after the Sabbath, when they could instruct those that had heard them on the Sabbath day.
Constantine was 300 years after Christ, and the results of his reign were really awful. He tried to help the church in every way he could, and it appears to me he was quite sincere about that. Nonetheless he harmed it. He harmed it badly.
He was trying to help the church. He knew they met on Sunday and that they had been meeting on Sunday for nearly 300 years. (Again, this is different than having a Sunday Sabbath.) So, as an act of kindness, he offered to make the first day a day of rest for the empire rather than the day of Saturn, which had been the day of rest back in the 2nd century.
Constantine wasn't trying to create a new Sabbath any more than earlier Christians were. He was trying to pay respect to the Church.
Like I said the end result of all his respect was great destruction to the church, and it did indeed lead to a Sunday Sabbath.