As long as humans have been mobile, we've looked for ways to make travel more pleasant. Litters (wheelless vehicles carried by porters, also known as palanquins or sedan chairs), used in ancient times, were often outfitted with cushions, a chair or couch, or even an enclosed cabin, allowing passengers to travel in comfort. It wasn't very comfortable for the litter-bearers, but that wasn't the point.
The first suspension systems for wheeled vehicles were iron chains or leather straps attached to the frame of a cart or carriage. These braces allowed the platform to stay separated from the frame, eliminating the worst of the bumping and rocking. Leaf springs—arc-shaped lengths of steel centered on the vehicle axle—began appearing on carriages in mid 17th-century France.
And don't forget the wheels themselves! Early methods of shock-absorbing included making wheels with fewer spokes—so the wheel would deform and flex more—and/or wrapping them