Let us now test this day and month from the Bible
On which day did the children of Israel arrive at the wilderness of Sin?
(Exo 16:1) And they took their journey from Elim, and all the congregation of the children of Israel came unto the wilderness of Sin, which is between Elim and Sinai, on the fifteenth day of the second month after their departing out of the land of Egypt.
(Exo 16:2) And the whole congregation of the children of Israel murmured against Moses and Aaron in the wilderness:
(Exo 16:2) And the whole congregation of the children of Israel murmured against Moses and Aaron in the wilderness:
What was then given to them?
They were fed with Manna, but here they were also reminded to keep the SABBAT DAY.
(Exo 16:23) And he said unto them, This is that which the LORD hath said, Tomorrow is the rest of the holy sabbath unto the LORD: bake that which ye will bake today, and seethe that ye will seethe; and that which remaineth over lay up for you to be kept until the morning.
(Exo 16:24) And they laid it up till the morning, as Moses bade: and it did not stink, neither was there any worm therein.
(Exo 16:25) And Moses said, Eat that today; for today is a sabbath unto the LORD: today ye shall not find it in the field.
(Exo 16:26) Six days ye shall gather it; but on the seventh day, which is the sabbath, in it there shall be none.
(Exo 16:27) And it came to pass, that there went out some of the people on the seventh day for to gather, and they found none.
(Exo 16:28) And the LORD said unto Moses, How long refuse ye to keep my commandments and my laws?
(Exo 16:29) See, for that the LORD hath given you the sabbath, therefore he giveth you on the sixth day the bread of two days; abide ye every man in his place, let no man go out of his place on the seventh day.
(Exo 16:30) So the people rested on the seventh day.
(Exo 16:24) And they laid it up till the morning, as Moses bade: and it did not stink, neither was there any worm therein.
(Exo 16:25) And Moses said, Eat that today; for today is a sabbath unto the LORD: today ye shall not find it in the field.
(Exo 16:26) Six days ye shall gather it; but on the seventh day, which is the sabbath, in it there shall be none.
(Exo 16:27) And it came to pass, that there went out some of the people on the seventh day for to gather, and they found none.
(Exo 16:28) And the LORD said unto Moses, How long refuse ye to keep my commandments and my laws?
(Exo 16:29) See, for that the LORD hath given you the sabbath, therefore he giveth you on the sixth day the bread of two days; abide ye every man in his place, let no man go out of his place on the seventh day.
(Exo 16:30) So the people rested on the seventh day.
Please read the whole of chapter 16
We know they entered the wilderness of Sin on the 15th of the Second Month (Exo 16:1)
(Exo 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.
(Exo 19:2) For they were departed from Rephidim, and were come to the desert of Sinai, and had pitched in the wilderness; and there Israel camped before the mount.
(Exo 19:3) And Moses went up unto God, and the LORD called unto him out of the mountain, saying, Thus shalt thou say to the house of Jacob, and tell the children of Israel;
(Exo 19:4) Ye have seen what I did unto the Egyptians, and how I bare you on eagles' wings, and brought you unto myself.
(Exo 19:5) Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine:
(Exo 19:6) And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
(Exo 19:2) For they were departed from Rephidim, and were come to the desert of Sinai, and had pitched in the wilderness; and there Israel camped before the mount.
(Exo 19:3) And Moses went up unto God, and the LORD called unto him out of the mountain, saying, Thus shalt thou say to the house of Jacob, and tell the children of Israel;
(Exo 19:4) Ye have seen what I did unto the Egyptians, and how I bare you on eagles' wings, and brought you unto myself.
(Exo 19:5) Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine:
(Exo 19:6) And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
It is therefore clear that it was on the FIFTEENTH DAY OF THE THIRD MONTH that they came to the to Mount Sinai and where Moses got the covenant of Yahweh
From the book of Jubilees, we have another witness.
(Jub 15:1) And in the fifth year of the fourth week of this jubilee, in the third month, in the middle of the month, Abram celebrated the feast of the first-fruits of the grain harvest.