The whole Israelite community set out from Elim and came to the Sin desert, which is located between Elim and Sinai. They set out on the fifteenth day of the second month after they had left the land of Egypt.
References for Exodus 16:1
The whole Israelite community complained against Moses and Aaron in the desert.
The Israelites said to them, "Oh, how we wish that the LORD had just put us to death while we were still in the land of Egypt. There we could sit by the pots cooking meat and eat our fill of bread. Instead, you've brought us out into this desert to starve this whole assembly to death."
Then the LORD said to Moses, "I'm going to make bread rain down from the sky for you. The people will go out each day and gather just enough for that day. In this way, I'll test them to see whether or not they follow my Instruction.
On the sixth day, when they measure out what they have collected, it will be twice as much as they collected on other days."
So Moses and Aaron said to all the Israelites, "This evening you will know that it was the LORD who brought you out of the land of Egypt.