Did immigrant women have special immigrant hospitals to birth their children? I am having hard time finding records of my Grandfather birth in Chicago in 1871. Parents were reported to be from Riga Lativia.
He may have been born at home.
This Wiki article may be helpful: https://www.familysearch.org/wiki/en/Chicago_Birth_Certificates
Also, this group in the FamilySearch Community may be of interest to you. Scroll down and look for the blue Join button on the right side.
@Jill P Smith if you want to share names and details, we may be able to help. While he may have been born at home, there may still be a birth registration or a baptismal record.
His name was Edgar W Smith (Calais), born in Chicago on 8/7/1884. I found one record on FamilySearch.com, but my dad said that his Grandparents were from Riga Lativa.
With Latvian roots, the surname might be spelled Kalē or some close variant.