Thank you for posting your question on History Hub.
The National Archives and Records Administration preserves and makes available the historically valuable records of the federal government. The federal government did not formally exist in the United States of America until the constitution was written and ratified; therefore, we do not have records from before the late 1700s. Records from this earlier time period would be stored in state archives, local libraries and historical societies.
An online search found several private websites that list Puritan migrations and even names of passengers on different ships from the 1620s through 1640s. We recommend performing online searches for these sites.
Additionally, historical societies and archives such as the Liberty County Historical Society have information on Puritan ships.
We hope this information is helpful in your research.
The National Archives and Records Administration