During the reign of King Henry VIII in the 1500s, he established the Church of England --- a new church that carried different practices from the Roman Catholic Church. And that time, he mandated all the residents in England to be part of this new church. The pilgrims were not open to this new mandate as they wanted to have the freedom to observe their religion. With this in mind, they decided to leave England and go to America where they will be able to start a new colony and be able to live and worship as Christians.
To add to this, given that they will be leaving as a community with their families in tow, they believed that they would flourish altogether. During that time as well, the Pilgrims were in talks with financial investors who could possibly provide the means for them to start a new life in America.
These are the reasons why they felt that they would be successful in America.