Question

how can you say that the lives of earliest people became easier on domesticating animals

Answer 1

Yes we can say that the lives of earliest people became easier on domesticating animals because-:

✨They can provide them with food.
✨They help them in pulling carriages.
✨They are trustful so they can protect them from other animals

Answer 2

I wont say that the lives would be easy in early days there are many disadvantages of domesticating animals
But taking about advantages 
They don't need fuel to run and there are trustful and they can return to there homes when they get lost. so this make  there lives a little easier.