It is difficult to put a precise timeline to any of the events of Exodus. There is little in the way of extra biblical material we can use to synchronize events; and what little we have allows only for imprecise measurement.

The Exodus narrative moves pretty quickly through a series of transitions from the initial move into Egypt (Gen 46:1–27) to the enslavement of the Israelites. The expansion of Israel's population could not have happened over night.  

The Exodus appears to happen during the early years of Egypt's New Kingdom period. The first mention Levantine people (AAMU in Egyptian) moving into Egypt dates from Tomb BH3 in Beni Hasan. This is the tomb of a functionary known as Khnumhotep II, and it depicts these people relocating to the Nile Delta. 

Over the next few centuries, various people from the Levant (or Canaan) moved into the Delta. At one point, there was a political shift and one of these groups claimed the Delta as an independent kingdom. Today, these people are called the Hyksos Kings. They ruled from Avaris. Eventually, a pharaoh named Ahmose (around 1550-1525 BC) claimed to have defeated the Hyksos and driven them out of Egypt, although the archaeological record shows no signs of such a defeat.

The Sons of Israel were likely a part of the this population of AAMU/Hyksos, and if so, then Ahmose or one of his successors may have been the "new king, who did not know Joseph" (Exod 1:8). If the Israelites did not depart with the rest of the AAMU population, they would have been enslaved as described in Exodus.

While Exodus lists the activity of building "store cities" (Exod 1:11), this is likely a shorthand for their entire role since they not only were involved in building but also "all kinds of work in the fields" (Exod 1:14). This likely describes mining in the Sinai, which was a source of great wealth for the Egyptians. People who spoke languages like Hebrew (called Northwest Semitic languages) are known to have worked there, and they have left behind some of the earliest fragments of a written alphabet.

Why did Pharaoh decide to have the Hebrew midwives kill the male newborns and not the females? One of the hallmarks of ancient societies was the way they absorbed other populations through child birth. When you took a city, it was fairly common to kill all the men and boys, but to take the women and girls as slaves or wives. When they had children with the conquering men, the children were trained to be part of the conquering society.

The midwives' refusal and their description of Hebrew women as "vigorous" (Exod 1:19) may not be a lie, as some commentators propose. The word translated as "midwife" is YELED, which just means they assisted in births. Such assistance may have been necessary in Egypt, which was a very old, closed society. Such societies tend to have problems with childbirth rates. The young, energetic Israelite population, however, was clearly not having those issues. If the midwives simply waited until being called, they would rarely be called by the Hebrew women.

It is worth noting that YHWH is present and active in Egypt here. "God dealt well with the midwives...and because the midwives feared God, he gave them families" (Exod 1:20–21). While the Israelites cry out under the burden of their slavery as if God is not present, he is there just as he promised Jacob he would be. 

If God was present in Egypt while the people of Israel suffered in slavery, some people might ask why he did not interfere. The better question might be, why didn't the people of Israel acknowledge him? What was going on with them in Egypt that they did not know their God?

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