Listing some of the records in case it helps someone finding more...
This is the social security application:
Name Frank C Olson
Birth Date 19 May 1863
Birth Place Sweden
Claim Date 16 Aug 1946
SSN 501109263
Notes 07 Jul 1978: Name listed as FRANK C OLSON
SSN prefix 501 means North Dakota. I assume you have a copy of it? So this is the one stating father as John M Olson and born Gothenburg. And his full name as Frank Charles Olson.
Gravestone says birthday is May 18th 1864 (obituary uploaded here as well):
https://www.findagrave.com/memorial/62374191/frank-c-olsonObituary states he came to St Paul, MN when he was 9 years old. No mentioning of any parents or siblings.
I assume you have a copy of his death record? And it states father as Frank Evenson? Who was the informant on that death record?
Personally, I would give more weight to his social security application since he added that info himself. Still it doesn't have to be correct.
Looking through the different census records the immigration year varies a bit. 1871-1873.
Worth noticing is that in the 1910 census it says that his marriage to Louisa is his 2nd.
I found their marriage record from May 12th 1897 and in it he has left both his parents blank while Louisa has listed hers:
https://www.ancestry.com/discoveryui-content/view/91792798:61484Only states he was living in Eau Claire and occupation tinsmith.
City directories from Eau Claire places him there already in 1891, so he should be in the Wisconsin State census from 1895.
There is a marriage record for Frank C Olson and Emma Mary Helbig April 10th 1893 in Eau Claire:
https://www.ancestry.com/discoveryui-content/view/1791535:61484?tid=&pid=&queryId=85998172-65d8-4f83-9c43-d971d984a226&_phsrc=sln16&_phstart=successSourceHe is a tinner. Lists his father as John M Olson. And in the place for his mother it just says deceased unfortunately.
Emma Maria Olson (Helbig) died 1895:
https://www.findagrave.com/memorial/242372443/maria-olsonSo, we have maybe two records where father's name is John M Olson and where the information came from Frank. And his mother died before 1893. He state himself he was born May 19th 1863 (if there isn't any transcription error) while his gravestone and death record says May 18th 1864.
Frans or maybe Fritz could be Frank in the US. He could also have taken that name himself. I haven't found any interesting Frans just yet and searching for a Carl with uncertain birth date is difficult...