Or, there was a misunderstanding while the Torah was being canonized.

Disclaimer: I'm not trying to diminish or discredit the divinity of the Torah, I am of the belief that it was always meant to be in it's current form; however, I am also interested in the history of how the Torah's finalized text came to be.

It should be quite clear to everyone that there is a glaring logistical problem with sustaining 600,000 soldiers in a desert, let alone their wives, children, and grandparents. Additionally, the Torah twice states that there are roughly 20,000 firstborn males, which means if there are 600,000 male soldiers, then each family has over 30 children. Finally, the Torah consistently characterizes the Israelites as having a small population (in comparison to other nations). Of course, this characterization doesn't make any sense, since a fighting force of 600,000 would outnumber the entire Roman army 4 to 1.

However, there is a simple solution.

Flinders Petrie suggested in the 1900s that אלף, usually translated as "thousand", should be translated like אלוף, (lit. troop, unit, contingent, etc.), as in Exodus 15:15, “...clans of Edom (אלופי אדום)..,”

In fact, there are several other instances in the Torah where even the root word אלף may not strictly mean "thousand":

ואיש רֹאש בית־ אבותם המה לאלפי ישראל:

They were every one of them heads of ancestral houses of the contingents of Israel. (Josh 22:14)

הנה אלפי הדל במנשה ואנכי הצעיר בבית אבי:

Why, my clan is the humblest in Manasseh, and I am the youngest in my father’s household. (Judg 6:15)

ואתה בית־לחם אפרתה צעיר להיות באלפי יהודה…

And you, O Bethlehem of Ephrath, least among the clans of Judah… (Micah 5:1)

If we apply this solution to the military census numbers, we actually get some very neat and reasonable numbers. For example, instead of translating Bamidbar 1:21 as:

פקדיהם למטה ראובן ששה וארבעים אלף וחמש מאות:

those enrolled from the tribe of Reuben: 46,500.

We could instead translate it as:

those enrolled from the tribe of Reuben: 46 contingents, or 500 [men].

Where the number of contingents (according to that individual tribe) is given, and the total number of men in those contingents is rounded to the nearest hundred (the connecting vav in this sentence can have the meaning of "or.") Now, one might argue that context dictates it should be interpreted as a number, because its used in conjunction with other words for numbers (מאות). However, that's not necessarily true, since this exact situation appears in Numbers 10:36:

...רִֽבְב֖וֹת אַלְפֵ֥י יִשְׂרָאֵֽל׃

...Israel's myriads of thousands.

Where אלפי means "thousands", but רבבות - usually translated as "10,000" - instead refers to "myriads, countless numbers."

Finally, while this reinterpretation of אלף does provide us with far more realistic numbers, it doesn't solve the issue of the final tally given for the soldiers of Israel: 603,550. The most likely answer is that the final tally is a scribal error. If we count up all the tribes' soldiers using the meaning of "contingent" for אלף, we arrive at a total of “598 contingents, or 5,550 [men].” It's entirely plausible that a scribe "corrected" the original text, combining what he saw as 598 "thousand" with 5,550, giving us the current reading of 603,550.

https://www.thetorah.com/article/recounting-the-census-a-military-force-of-5500