Have you tried searching under the spelling "Neilsen"? I get a ton of search hits that way who were born in Denmark in 1885, even some who have an arrival date within 2 years +/- of 1902. Do you have any other means of identifying whether you have the right one?
Thanks for the suggestion. Yes, I have tried the varients of the surname Nielsen (Nielson, Neilsen, Neilson, Nilson, Nillson, Nelson etc.). At this time there are so many to count! Because there are so many possibilities, I am concentrating on the date of birth. I am also looking in California, New York, and states that have had large Danish populations. If you come up with other suggestions, please let me know. I usually find at least one record for people but this one has me stumped!