Commentary for Exodus 19:15

היו נכנים לשלשת ימים means be ready by the end of three days, that is, by the fourth day — for Moses added a day of his own accord to the time appointed by God. This is the opinion of Rabbi José. But according to the opinion of him who says that the Ten Commandments were given on the sixth of the month Moses did not add anything, and the words לשלשת ימים do not signify after three days but mean the same as ליום השלישי (v. 11), i. e. by three days (cf. Shabbat 86b-87a).

By the end of three days. . . [Rashi knows this] because it is not written ליום השלישי , as Hashem commanded Moshe — but rather לשלושת ימים , implying when three days have already passed.