When was something we would recognize as 'string' invented? What about ropes and general string-like or rope-like things? What were older versions like? What were they made out of? How common or available would they be?
It's tough to answer this question based on physical evidence alone, as most materials that are used to make string (plant and animal fibers) degrade relatively quickly. The oldest direct evidence of string and its evolved form, cloth, are a few swatches of woven cloth that had been encrusted in carbonate in France ~16,000 bce and some cordage and string from the near east dating to ~17,000 bce.
That being said, we can infer the presence of string even further back from other archaeological remains. Looking at artifacts and human remains from the Gravettian culture (France, 26,000 to 20,000 bce) we see that needles became increasingly common, with smaller and smaller eyes as time went on, which indicates that there was some sort of string that was being sewn with.Furthermore human remains from the same period are often decorated with lines of beads or shells with holes in them, oriented in such a way that they suggest that they were originally strung on a string. It's likely that the earliest strings were made out of animal gut or sliced animal skin rather than twisted fibers, as we would thing of string today.
For early evidence of string made from twisted fibers, we again have to look for indirect evidence. A good piece attesting to the presence of fiber string is the Venus of Lespugue, an approximately 25,000 year old statuette from France. The figure is wearing a woven string skirt; the fibers are intricately carved to show not only the twist of the threads, but also fraying at the ends of the warp threads, which only happens with plant/animal fiber cordage, not with skin or gut string.
Archaeologists have also found clay shards that were left to dry on pieces of woven fabric, which left impressions of early textiles on a number of them, the oldest dating to 29,000 bc.
Of course these are the few pieces of evidence that have survived. Based on the relative sophistication that had already developed by this period, textile archaeologists posit that the use of string and woven fabric probably go back to the year 40,000 bce, at the very least.
A string/rope-like cord was a found at the French Paleolithic rock art site dating tens of thousands of year ago. It would be easy to imagine that the use of plaited cord is very old.