During the first century AD, was the first day of the week the one after Shabbat and was it what we now call Sunday?
The Torah tells us pretty clearly in Exodus 20:8-11 that the Sabbath must be kept on the seventh day of the week (see also Genesis 2:1-2).
Remember the Sabbath day to sanctify it. Six days may you work and perform all your labor, but the seventh day is a Sabbath to the Lord, your God; you shall perform no labor, neither you, your son, your daughter, your manservant, your maidservant, your beast, nor your stranger who is in your cities. For [in] six days the Lord made the heaven and the earth, the sea and all that is in them, and He rested on the seventh day. Therefore, the Lord blessed the Sabbath day and sanctified it.
(Translation from Chabad.org)
What the secular calendar calls "Saturday" is the Sabbath day for us Jews. It has never been on a different day in history past.