Hello everyone! I'm having trouble locating birth records and naturalization records of a great grandfather of mine who immigrated to the U.S. from Portuguese Cape Verde (likely sometime in the 1920s—possibly prior—but by 1928 he had been married in the U.S. and had a son.)

I've scoured FamilySearch, Ancestry, Fold3—I've found brief information about him in the 1940 and 1950 U.S. census which states his birthplace as being simply "Portugal" and nothing other than an anglicized version of what his name was. The 1940 U.S. census claimed his citizenship status as "naturalized" but I can't find any records that would support he'd been through the naturalization process. I located his WW2 draft registration card which contained the same level of information that I already knew—except now I have his exact birthdate (if the date he provided on his WW2 registration card was accurate.)

I now know his birthdate, anglicized name (I know his original surname but not his original given name), where he lived in the U.S. and who his spouse was but I can't seem to find any information about his own relatives, which island he was born on or any record of his birth or baptism at all. He was born in the year 1900.

Is there any way I can find out more about his immigration without having to pay archivists or the USCIS? Is there any way I can find records of his birth? If FamilySearch and Ancestry are not yielding the results I'm looking for. And my living relatives don't seem to know much information.