Well, I don’t read anything in the primeval history that indicates what the several academics have suggested in your OP. The focus from the start seems to be more agrarian. Even before God created Adam, it is said ‘and there was no man to till the ground’ (Gen. 2:5). And then after God created Adam, God placed Adam in the garden of Eden ‘to till it and to keep it’ (Gen. 2:15). After Adam and Eve’s sin and expulsion from the garden of Eden, God said to Adam ‘cursed is the ground because of you; in toil you shall eat of it all the days of your life; thorns and thistles it shall bring forth to you; and you shall eat the plants of the field. In the sweat of your face you shall eat bread till you return to the ground’ (Gen. 3: 17-19). The verse appears to indicate that Adam would have been both a farmer and a gatherer, a gatherer from the words ‘and you shall eat the plants of the field’.
Cain and Abel are the first two sons of Adam and Eve recorded for us. And the scripture reads ‘Now Abel was a keeper of sheep, and Cain a tiller of the ground’ (Gen. 4:2). Both of these occupations are more agrarian than hunter-gatherer. But Cain murders his brother Abel and for his punishment God says “When you till the ground, it shall no longer yield to you its strength; you shall be a fugitive and a wanderer on the earth” (Gen. 4: 12). So Cain went from tilling the ground to being a fugitive and wanderer on the earth and possibly a hunter-gatherer or just a gatherer of plants for food. The first son of Cain recorded in the scriptures is Enoch and ‘he built a city’ (Gen. 4:17).
In conclusion, the primeval history of the first humans in Genesis mentions tilling the soil, farming, and keeping livestock but nothing about hunting. In fact, if I’m not mistaken, the first mention about humans eating meat in the scriptures is after the Flood in the account of Noah. In the Genesis 1 creation narrative and upon the creation of man and woman, God says “Behold, I have given you every plant yielding seed which is upon the face of all the earth, and every tree with seed in its fruit; you shall have them for food” (v. 29). From the biblical account, it appears that the first humans were vegetarians.