Absolutely women did this (and textiles -such as carrying baskets, storage vessels & clothing) and traded the excess with other families, thus creating markets.
I'm convinced that tanning, and eventually textiles we're invented by women to carry babies and toddlers. I've got five kids and man you can't do shit with a baby around unless you wear them. It would have been a top priority for ancient women, to keep their babies close and safe while having their hands free
There's a book, women's work the first 20,000 years, that you might like.
I don't remember it making claims about the invention of agriculture, but it's quite clear that early agriculture (before the plow) was traditionally women's work.
He missed out women inventing horticulture / farming.
I'm convinced it was women who started farming: traditionally women primarily undertake gathering - finding roots & tubers, gathering seed & grain, etc. So women will have primarily been the ones digging up roots & tubers - and by trial and error discovering how to increase the yeild from the wild foods they were gathering.
Firstly they'll learnt that you need to leave some tubers in the ground to ensure there will be food next season. They'll have gradually learnt that clearing a patch of ground, losening the soil, and replanting small tubers instead of harvesting them would increase the yeild when they returned to harvest again in the next year / season. They would have been doing plant husbandry as they gathered - and from this, horticulture / farming would be born.