The Torah (Exodus 20:8-11) commands:
ח: זָכוֹר אֶת יוֹם הַשַּׁבָּת לְקַדְּשׁוֹ: ט: שֵׁשֶׁת יָמִים תַּעֲבֹד וְעָשִׂיתָ כָּל מְלַאכְתֶּךָ: י: וְיוֹם הַשְּׁבִיעִי שַׁבָּת לַה' אֱלֹקיךָ לֹא תַעֲשֶׂה כָל מְלָאכָה...: יא: כִּי שֵׁשֶׁת יָמִים עָשָׂה ה' אֶת הַשָּׁמַיִם וְאֶת הָאָרֶץ אֶת הַיָּם וְאֶת כָּל אֲשֶׁר בָּם וַיָּנַח בַּיּוֹם הַשְּׁבִיעִי עַל כֵּן בֵּרַךְ ה' אֶת יוֹם הַשַּׁבָּת וַיְקַדְּשֵׁהוּ
(8) Remember the Sabbath day and sanctify it. (9) Work for six days and perform all of your labor. (10) And the seventh day will be sabbath for God your Lord. Do not perform any labor... (11) For in six days God made the heaven and the Earth-the sea, and all that is in them, and he rested on the seventh day. Therefore he blessed the Sabbath and sanctified it.
Evidently, the cycle of 6 days of work and 1 day of rest commemorates God's activities. I have assumed that 6 work days are the six days that God worked, and the seventh is the day that he rested.
Accordingly, upon receiving the command to keep Shabbat, the Jews either began resting on Saturday which had been preserved as the seventh day of the week-cycle since the creation of the world. Or, they were informed of which day had been the seventh and began resting on it.
My question is: is this assumption correct (and if so did they continue the existing week cycle, or had it strayed necessitating a realignment of the seventh day to the historical Shabbat), or perhaps was the Jewish halakhic week-cycle independent of the historical week.
An alternative possibility, if the halakhic week were independent of the historical week, would be that the Jewish people were commanded to work for 6 days starting at some point (perhaps the Sinaic revelation) and rest on the seventh. Accordingly, the seventh day would not necessarily be the same day of the day of God's rest.
related: this question which assumes that the Sabbath is aligned with the original day 7.