Did early humans ride on the backs of animals to get from place to place more quickly?

No, our prehuman ancestors that appeared a million or more years ago through the first modern humans that appeared about 100000 years ago only went from place to place by walking on their own two feet.

Humans did not begin domesticating any animals other than dogs until shortly after the end of the last ice age, about 12000 years ago. Dogs were domesticated about 15000 years ago, to assist hunter-gather peoples. But humans cannot ride on the backs of dogs.

The first animal domesticated that humans rode on the backs of to get from place to place more quickly was the horse, this did not happen until about 5500 years ago in what is now the Akmola Province of Kazakhstan. These people were fully modern humans (in no way "early humans") that first domesticated and rode horses.