Well actually.....
I carried my Urchling around in a pouch for the most part, I saved up money before I had her so I could stay at home with her, she nurses on demand, slept with me, secured safely by a pool noodle duct taped to the mattress, and was carried around the bulk of the day. Largest stretches of time where she wasn't in direct contact during those early months was in the car.
Basically, I chose what we could refer to as the prairie or Orangutan method of infant care over the more "modern" Spock or Dobbs method.
It's true that I have more fat in my diet than my prehistoric ancestors but you also need more than fat in your diet to produce milk.
I bought a pacifier two pack which she forcefully rejected and 2 bottle 3-packs. I think I opened one of them up for water/juice once she got a little older.
I did not menstruate again for slightly over a year.
I'm also very outdoorsy. We were out hiking and fishing at 3 months. Baby backpacks are awesome.
I'm also familiar with what's required to hunt successfully, even though I don't hunt myself. If I track an animal it's to tag, measure, or observe them. BS Wildlife Science.
So no offense, I think I understand the complexities involved for both sides of the equation far better than most.
Would it be more challenging than sans infants/children? Yes. Impossible? Not hardly.
The man as hunter myth focuses on megafauna and other large herbivores so much, people tend to forget there was plenty of smaller game as well. Pregnant women and nursing mothers may well have focused on smaller game during that time frame of her child's life but a grouse, a small gazelle, a bezoar ibex, squirrels, or rabbits are food and protein every bit as much as a moose or a wooly mammoth is. Smaller game can also more successfully be bagged by trap hunting. And that's still hunting.
Babies on your back will likely be a hindrance for spear hunting, but not bow and arrow, sling shots, or other such devices. It's doable.