According to this Omer is 2.5 liters or more. This is too much bread per person as specified in Shemot 16:16? How do traditional sources justify the value of Omer? Shemot 16:4,8,12,15 e.t.c calls it bread for food and bread from heavens so it have to be comparable to wheat or barley.
Actually, that's not that far off -- about a factor of two.
Archaeologists tell us that an ancient Israelite ate about 330-440 pounds of wheat and barley per year. Since the Israelites in Sh'mot were active all day (nobody's sedentary in a moving camp), let's assume the upper end of that -- it might have even been somewhat higher.
2.5 liters of barley is about 3.3 pounds and 2.5 liters of wheat is about 4 pounds (source, plus math). This then has to be ground for flour, porridge, and other uses, during which process there is some loss.
The torah talks about "bread" (actually לֶחֶם) but it doesn't mean they went out and picked loaves of fresh-baked bread; the man provided ingredients. Further, given the miraculous nature of the man in the first place, I don't think we need to assume that it consisted only of grain for bread. I know you're not interested in rabbinic interpretations, but there is one that says the man took on whatever flavor the eater desired. This could be true of form too.
So, bottom line, if they started with about 3.5 pounds of grain-equivalent per person and turned it into food, that's not too far out of line for the Israelites in the wilderness.
I think some of the sources show a larger omer than what could be possible, too. I posted this link on another thread, but my husband and I did an extensive study in 2015 to determine what size the omer would need to be to fit all the constraints listed in the Bible, and a few more in Josephus' writings. We considered a simulated mannah, adding oil and honey to basic grains, and getting an estimated caloric value. Then, by using the "average" calories needed for men and women, we "back-calculated" what size the omer would need to be.
We repeated this process for all the other constraints, such as: recipes between the hin and omer to make the unleavened bread for the grain offerings, dedication offering for Aaron and his sons, and the firstfruit offering of yeast bread. Also, using the size of barley grains, and the average size of fingers for the estimate of the etzba, the size of the showbread listed by Josephus, and the measurements of the table of showbread, a daily ration of water, plus more. The final result is that an omer was somewhere between 3-4 C, with an average of 3.4 C. This is roughly equivalent to the amount that comfortably fits into a quart canning jar, and not up to the very top.
Please see our paper describing all the experiments and results here: http://readyanswers.org/PathfinderBibleExperience/Exodus/ConstraintsHinOmerEphah.pdf
The paper also discusses the hin and the ephah.