What did people living in paleolithic times use to tie stuff together

Sinew and twine. Sinew or Tendon is a connective tissue that holds bones and things in place in animals. So you kill a deer and you cut out some of it’s sinew to use as cord. It has good properties, waterproof, natural glues and is very tough.
Twine is made from plants or wool and is still widely used today. You just get the fibers together and make yarn from them by spinning then twist into thicker twines and strings and ropes.