Clothes from 8k Years Ago Were Made from Trees, New Research Suggests
gizmodo.com
gizmodo.com
Wikipedia has an article (1) and pictures of modern bast fiber weaving in Norway.
Something that really is coincident with the end of the last ice age (technically, the end of the 1200-year Younger Dryas cold spell brought on by a bolide strike on the North American ice sheet) is Gobekli Tepe. That was, thus, built some 2000 years before this fabric was made. The 200m sea level rise that started ~20kya was ending about then, with the final bits of what had been the Persian Gulf river valley filling in.
Apparently, someone wrote a paper about it: "Barkcloth in India-Sanskrit Valkala", https://www.jstor.org/stable/597920
Just imagine being at 30° with leather jacket + pants pursuing some damn fast animal for a couple of miles. You NEED lighter clothes.
Palms are not members of the grass family (Poaceae) though.