Dear Ms. Christy,
Thank you for posting your request on History Hub!
As death certificates often include parent names, we suggest that you request a record search from the California Department of Public Health for records of Fred James Dupont, his siblings and his mother. In addition, the FamilySeach research wiki for California Vital Records may be helpful.
We also suggest that you search the 1902: Directory of City & County of Honolulu and other directories available online, Hawaii Marriages, 1826-1922, the Hawaiian Genealogy Indexes for mention of Antone Vierra, Mary Freitas and Manuel Dupont and request a record search from the HAWAIʻI STATE ARCHIVES. The FamilySearch Research wikis for Hawaii, United States Genealogy and Portugal Genealogy also may be useful.
Lastly, we suggest that you review these Genealogy: Passenger Arrival List Research Tips and NARA’s page on Immigration Records for suggestions on how to locate passenger information for Mary Freitas Vierra Dupont. There are numerous ways that individuals could enter the United States such as on a ship that arrived at various coastal ports or over land from Canada, etc. Ship passenger arrival lists were a requirement beginning in 1820, but that does not guarantee that person was recorded or that the list still exists. Many of the passenger lists have been digitized and are name-searchable online using Ancestry and FamilySearch. There may be a fee for using Ancestry. Instead, you may wish to contact your local library. Many library systems subscribe to these sites, making them free for patrons.
We hope this is helpful. Best of luck with your family research!