For the most part, white people coming in the 1600s to the British colonies in what would later become the United States were not forced to come. Not all of them were free when they arrived, but most of them were not forced.
There were some people who were forced to come to North America. In the 1600s, there were some people who were sent to America as punishment for crimes. At that time, a person could be sentenced to “transportation” from England for a given number of years. Some of these people were sent to North America. They represented the main group of white people to come involuntarily.
Some white people came voluntarily but were not free. These were the indentured servants. These were people whose prospects in England were bad enough that they were willing to sign up as indentured servants. These people were essentially slaves for a set number of years (often seven years) to the person who paid their fare to the New World.
All other white people came to North America on a completely voluntary basis. There were many different kinds of people who came, but they were, generally speaking, not forced to come except for the criminals being punished.