Paleolithic people wore clothes out of leather, since it was plentiful from hunting. They also used high-tech sophisticated sewing to make it into actual garments. They used different types of skin and leather treated in different ways (dried, boiled, tanned, cured). Thicker, heavier leather such as buffalo was used for shoe soles. Elk or bull would be used for the upper, and clothes worn on the skin (as opposed to outer clothing) would be of soft material such as goat or lambskin.

Comment: Good question
Question for answerer: How can paleolithic people be all high-tech when they lived in early stone age?
Answer: They sharpened bones of animals to use as needles to poke holes in the leather, then used thin strips of leather (cut with stone tools) to weave through the holes. They used every part of the animal they hunted. Including using tendons as sinew (like a strong string for tying things tight). Not enough credit is given to stone-age people, they were incredibly resourceful and much more intelligent in the ways of our world than the vast majority of the world is today.

There is also some speculation and evidence that they made string and braided or knotted it into clothing, baskets and nets, dating back 29,000 years or more.