During the time of Joseph, Jacob's extended family migrated to Egypt. Some 70 members of that extended family are mentioned in Gen 46:8-17, almost all of them being male. So perhaps the total number of people who went to Egypt was something like 150.
The family prospered in Egypt and grew quickly (Exod 1:7), consistent with God's promises to Abraham (Gen 15:5). At some point the Egyptians used the success of the Israelites as an excuse to enslave them, but their numbers continued to grow (Exod 1:20) despite Egyptian attempts to limit their population.
The Israelites were in Egypt for several generations. 1 Chron 7:23-27 lists eleven generations from Joseph to Joshua, for example---counting Joseph as generation zero, Ephraim as generation 1, etc. (The three-generation Levi-Kohath-Amram-Moses sequence summarized in Exodus 6 probably skips a number of generations, as biblical genealogies sometimes do.)
Our English translations tell us that "about six hundred thousand men" left Egypt on the Exodus, which would give an Israelite population of a few million at that point (Exod 12:37). Exodus 38:26 lists a more precise figure of 603,550 adult males, consistent with Num 1:46.
Some other scriptures call our English translations into question, especially when we take into account the data we have about populations in that area and region.
In particular, Num 3:43 gives the number of firstborn males at least a month old as 22,273. With the total number of males presumably being over a million, we would expect the number of firstborn males to be something on the order of 10 times bigger than 22,273.
Another question arises in Exod 23:29-30, where God says that he will drive the Canaanites out of the land slowly, since Israel's population isn't sufficient to drive them out all at once. But if there actually were millions of Israelites, then they would have had plenty of people to fill the whole land immediately.
Another passage that suggests a smaller population is Deut 7:1-7. Verse 1 lists seven peoples in the land and calls them "seven nations more numerous and mightier than you." Verse 7 states, "It was not because you were more in number than any other people that the LORD set his love on you and chose you, for you were the fewest of all peoples."
More problems are apparent when we start considering what we know about geography and populations in that region.. (Michael Heiser gives good coverage of the problems in Episode 271 of his Naked Bible Podcast.)
Here is one example that he mentions. Before crossing the Jordan into the Promised Land, the Israelites "camped by the Jordan from Beth-jeshimoth as far as Abel-Shittim in the plains of Moab" (Num 33:49). Since those two locations are about 7 miles apart, the camp could have covered up to 49 square miles. But putting a population of two to three million people in that space would require a greater population density than in present-day New York City, without the help of multi-story buildings. There would be a similar problem with the area where the Israelites camped right after they crossed the Jordan.
After the Israelites reached the Promised Land, the first place that they conquered was Jericho. Jericho seems to have been a small, strategically located fort. Conservative Bible scholar Richard Hess estimates the size of the garrison stationed there at about 100. Hess also talks about numbers from the Amarna correspondence, letters sent from the city-states of Canaan to the Egyptian Pharaoh during the late Bronze Age. The leaders of the city-states sometimes request that Pharaoh send them troops, and the numbers of troops they requested tend to be no more than a few hundred and are often smaller. If such a number of soldiers was significant, populations of cities in Canaan couldn't have been too large at that point.
Two main options have been proposed for solving this numbers problem. One is the possibility that eleph, the Hebrew word translated "thousand" in Exod 12:37 and Num 1, might not mean "thousand" in this case. The word can also mean "cattle" (Deut 7:13; 28:4,18,51), "oxen" ( Isa 30:24; Ps 8:7), "clan/clans" ( Josh 22:14; Judg 6:15; 1 Sam 10:19; Isa 60:22; MIc 5:2), "(military) division/divisions" (Num 1:16), "family", or "tribe".
In his commentary on Exodus, Douglas Stuart explains that the word started out meaning "ox," then came to include a group of oxen that gravitated around a particular ox, then came to stand for some group of people of indeterminate size, like a clan or a military division, then came to have the technical meaning of "thousand."
In the case of an army, a single division might be a group of men from one village. In that case, an eleph might mean ten or fifteen rather than a thousand. In Exod 12:27 the 600 elephs could have a lot fewer people than 600 thousand. Stuart suggests that with an eleph that averaged around a dozen, the total number of soldiers in Exod 12:37 could have been about 7200, and the total number of Israelites something like 30,000.
Another explanation involves the way that ancient documents, in describing military victories in particular, would exaggerate the numbers involved, for the purpose of exalting the king. It has been proposed that the Bible may have exhibited a similar hyperbolic use of numbers in order to emphasize how much God had blessed the Israelites.
Archaeologists estimate the population of ancient Israel by looking at the kind of houses that they had in those days, the number of people that could fit in such a house, and the amount of land that was available. When Wheaton College archaeologist Daniel Master visited Miami University in early March 2020 (just before the COVID lockdown) to give a lecture, I asked him about the population of ancient Israel. Master emphasized that these kinds of estimates are pretty rough. He gave me an estimate of 125,000 for the population of Israel in the time of David, which could be some 400 years after the Israelites arrived in the Promised Land, after the nation had had a lot more time to grow.
Based on all of this information, I'm inclined to agree with Stuart's estimate of about 30,000 for the number who left Egypt on the Exodus.
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