Very interesting timeline found at The New World Encyclopedia site:

c. 8000 B.C.E. – Evidence of flax cultivation in the Near East.[3]

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.[4] This requires much greater skill than knitting in order to create a fine product.[5]

c. 6000 B.C.E. – Evidence of woven textiles used to wrap the dead at Çatalhöyük in Anatolia.[3]

c. 5000 B.C.E. – Production of linen cloth in Ancient Egypt, along with other bast fibers including rush, reed, palm, and papyrus.[6]

4200 B.C.E. – Date of Mesolithic examples of Naalebinding found in Denmark, marking spread of technology to Northern Europe.[7]

c. 3000 B.C.E. – Breeding of domesticated sheep with a wooly fleece rather than hair in the Near East.[3]

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.[8]