Charles Olson aka Wilson b 1834 in maybe Oslo

Seeking the Norwegian roots of Charles Wilson (b 1834) of Brooklyn, Kings, New York. Born in Norway, with surname Olsen in Norway. We would appreciate any help so much! We’re looking for a ship’s crew list - or any evidence - that shows this ancestor coming from Norway to New York, USA. Even better would be his birth record, birth place, and family in Norway. We have already located the family in New York (see the online family history here: http://www.skippywilson.com/charles1.html) Charles Olsen was born 9 June 1834 in Oslo. At least family folklore says this was his birth place and birth name. In the USA he was called Charles Wilson. The family believes Oslo is his birthplace but have no proof of that. His death certificate states that his father’s name was Charles (perhaps an Americanization of a Norwegian name such as Carl or Claus). Family folklore tells that he entered the USA by “jumping ship,” which implies that he was a member of a ship’s crew. He appears as Charles Wilson in a Brooklyn, Kings, New York, city directory dated 1864, so he was in Brooklyn at least by then (and possibly earlier). His first child was born in May 1865 in Brooklyn. His wife was Catherine Reinhardt. Their twelve children were Caroline, Anne J., Charles John Jr., Mary, Annie G., Fannie, Lulu, Kate, Katrina, Fred, Martha M., and Ida Louise. An old family photo of him has a handwritten note on the back; a hard-to-read word appears in front of the word OSLO, that could say Christiansted? Christiansand? or Christiania? The cousin who owns the photo was told Charles's birth place was Oslo. Thanking you so much in advance for any help you can give!