The following is a reasonable time line combined with deductive reasoning that kills the traditional Pentecost theory.
The children of Israel departed from Ramseys on the 15th day of the FIRST month, Numbers 33:3, and they had reached the wilderness of Sin of the 15th day of the SECOND month. Judging from my map of the children of Israel's journey from Ramseys to the Wilderness of Sin is approximately 150 mi. these figures creates a math problem because if we have a distance of approximately 150 mi. being traveled in 30 days and by dividing 30 into 150 we get an average of 5 mi. per day.
If we assume that at least four of the 30 days were no traveling days/Sabbaths which leaves 26 travel days in which to cover the 150 mi. from Ramseys to the Wilderness of Sin and if we divided 26 into 150, we get almost a 6 mi. per day average which seems about right because a grown man can travel 15 to 20 mi. per day but when we consider women and children moving all their belongings alone with the gold and different treasures from Egypt, I believe we can safely assume that the children and women could not travel the same distance in a day as a grown man, maybe one half the distance which would be seven to 10 mi. per day. On top of this, herding the animals, sheep, goats, and cattle, not to mention any poultry etc. at any rate around 6 mi. per day seems reasonable for such a great multitude traveling in the wilderness, carrying everything they have, headed for a new land. And whether it seems reasonable to you or not , according to the pinpointed number of days and the distance, almost 6 mi. per day was the average, this is an absolute.
According to my map it is approximately 220 mi. from Ramseys to Riphidim, therefore we can conclude that it is approximately 70 mi. across the Wilderness of Sin to Riphidim. Now if we do the math, we see what would be the earliest date they could have arrived at Riphidim after leaving the wilderness of Sin.
The earliest they could have left that campsite after receiving manna for seven days would be on the 23rd of the second month because we know from Exodus 16, the weekly Sabbath was on the 22nd of the second month. According to the above information from my map and math, it would take them approximately nine days to make the 50 mi. journey at almost 6 mi. per day because six times eight is 48.
Assuming they left for the 50 mi. journey on the 23rd, the soonest they could have arrived in Riphidim would be on the 1st of the third month because one of the nine days would have been a weekly Sabbath of no travel. If they were murmuring on the Sabbath and the new moon days because after about a week their water was gone and if they got the miracle water around the new moon day of the third month, and Amalek attacked them, Moses said for Joshua to go out and fight him TO MORROW, which would be the second day of the third month, Exodus 17:8 and the battle lasted all that day which would bring us to the third day of the third month and they still have to travel from Riphidim to the mount. All this is assuming they received the water and fought with Amalek, and left the water with their wounded and thirst animals, all on the same day, which is highly unlikely if not impossible. Not to mention that Moses wrote a book and built an altar after this great victory, see Leviticus 23:12-15. The Scripture does not read all of these events concerning the murmuring for water and the fight with Amalek etc. was back to back on the same day but even if it was, they still had to travel to the mount and it was three more days before the people were spoken the commandments and anyone who cannot accept this combined with the other evidence, is in the state of denial to say the least.
Brother Arnold