Padded jacks, arming doublets, gambesons, buff coats, quilted armour. Whatever you call it, it’s likely the oldest form of armour in existence, as it is merely a form of ordinary clothing padded and toughened to make it resilient against weapons and deceptively functional as armour.
It’s important to differentiate between gambesons that are designed for wearing under armour and gambesons designed for wearing on their own. Items designed for use under armour usually focus more on improving comfort with heavy items on top and protect mostly with the cushioning alone, retaining maximum mobility under other gear that may well be fairly restrictive already. Padded coats designed as standalone armour on the other hand often have been toughened by various means to resist sharp slicing and puncturing, often at the cost of flexibility (though not enough to render the armour impractical of course).
Materials such as linen, wool, leather and even exotic materials such as cotton from the Americas and Silk from the Orient are suitable for resilient jackets and thick stuffing only makes them more absorbent against otherwise deadly weapons of war. It is noteworthy that on some artwork, forms of quilted and layered armour are seen no just under or instead of other armour, but sometimes even on top of it for yet another layer of tank-like defences!