Very interesting timeline found at The New World Encyclopedia site:
c. 8000 B.C.E. – Evidence of flax cultivation in the Near East.
c. 6500 B.C.E. – Approximate date of Naalebinding examples found in Nehal Hemar cave, Israel. This technique, which uses short separate lengths of thread, predated the invention of spinning (with its continuous lengths of thread) and requires that all of the as-yet unused thread be pulled through the loop in the sewn material. This requires much greater skill than knitting in order to create a fine product.
200 B.C.E. to 200 C.E. – Approximate date of earliest evidence of “Needle Knitting” in Peru, a form of Naalebinding that preceded local contact with the Spanish.