In the early colonial days who were able to earn their freedom after working a certain number of years

Slaves could win their freedom in three different ways during colonial days.

First, they could just run away but this was quite dangerous.

Second, they could buy their own freedom with extra money the saved.

Third they could be emancipated by their master after working a certain amount of years or simply for an extraordinary feat done in favor of their master.

So the answer is Slaves, slaves could win their freedom after working a certain number of years.

Indentured servants.

When the colonies were newly established, there was a need for cheap labour in British North America. This coincided with the end of the Thirty Years War, which meant that there was massive unemployment and poverty in Europe.  

These events lead to a system called “indentured servitude.” Workers would come to the US and typically work for around 4-7 years in exchange for passage, food and lodgings. It was a harsh and restrictive life. However, when liberated, a lot of them were able to achieve comfortable lives in the new colonies.

However, as the slave trade from Africa increased, indentured servitude decreased. African slaves provided a cheaper source of labor while enjoying less legal protection. As one type of forced labour rose, the other one decreased, until African slaves were the main source of labour in the American colonies.