Dear Mr. Silverstein,
Thank you for posting your request on HIstory Hub!
United States ports were not required to maintain departure passenger lists. As passenger names were occasionally listed in a newspaper for arrival port as traveling on a certain ship on a certain date, we suggest that you search the Cuban newspapers for mention of these passages.
We searched the National Archives Catalog and located the series Passenger and Crew Lists of Vessels Arriving at New York, New York, 1897-1957 (T715) in the Records of the U.S. Customs Service (Record Group 36) that may contain immigration information related to your search. For access to and/or copies of these records, please contact the National Archives at New York (RE-NY) via email at firstname.lastname@example.org.
T715 is available and searchable on Ancestry.com and FamilySearch.org, There may be a fee for using Ancestry. Instead, check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
We also searched the Catalog and located the series United States Diplomatic Records for Cuba, 1902 - 1935 in the Records of the Foreign Service Posts of the Department of State (Record Group 84) that may contain information about the people you seek. For access to these records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at email@example.com.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RE-NY and RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
The U.S. Department of State has passport applications from April 1925 to the present. We suggest that you visit their website Get Copies of Passport Records to request applications for the individuals you seek.
Lastly, the FamilySearch Research wiki for Cuba Genealogy may be useful.
We hope this information is helpful. Best of luck with your research!