"Exodus 19:1 In the third month, when the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai" (DLT: torahtimes.org).

third month: the first day of the third month was on the second day of the week.  This is according to Seder Olam, but also according to the Torah.  They traveled in the wilderness of Sinai for a three day journey, days 2,3,4, and they then were supposed to prepare for two days, 5, 6, and be ready for the third day, the 7th day Sabbath, on which they received the ten commandments.   After sunset, starting the Sabbath God spoke the words to them, and in the morning they had a feast and the seventy went up the mountain to see God.   The new moon day for Sivan in 1632 BC works out to be on the second day of the week.  Joshua's long day has no effect on the date of this new moon as the arc of vision was very large. (DLC: torahtimes.org)

Daniel's Literal Translation and Commentary: (http://www.torahtimes.org/translation/exo1901.html)