> How do I make the connection to earlier ancestors to apply to the Mayflower Society?

You do it in the only possible way - the way that research on one's ancestry is always done - you work backwards one generation at a time, consulting as many contemporary records as possible. If you are fortunate you will find an ancestor whose surname, time and place suggest possible Mayflower ancestry. You can then investigate published Mayflower research to try to confirm the connection.

Dale H. Cook, Member, NEHGS and MA Society of Mayflower Descendants;
Plymouth Co. MA Coordinator for the USGenWeb Project
Administrator of http://plymouthcolony.net