You should work backwards from yourself backwards to this "Carson" and then find who his parents, siblings, and other relatives were. It is much less efficient to try to trace downwards from a famous possible relative.
There is a book called "24 Famous Swedish Americans and Their Ancestors" and Charles Lindbergh's direct ancestry is listed. However, since you think your "Carson" is distantly related, it is best to find the ancestors of your "Carson" first since they won't be listed in the direct line of Charles Lindbergh. Then there are ways (sometimes very easy; sometimes not) to find where that person lived in Sweden (parish name) and then find that person's relatives. After that, it is worthwhile checking this book to see if there is a way to connect the ancestors you have with the ancestors Charles Lindbergh had.
Once you have enough information that you know a specific name for your "Carson"; when he was born (specifically) and a very narrow time line for when he emigrated (within a year or two or three) and specifically where he was known to live after leaving Sweden, (and other details such as those), then post a query on the Sweden forum (also on Genforum) and there may be a way to find where your "Carson" lived in Sweden.
The following site tells the type of information you generally will need to find information in Swedish genealogical records.
The 1900-1910-1920-1930 U.S. Federal Censuses provide a year (usually approximately correct, within a few years) of immigration. The 1900 U.S. Federal Census provides a month and year of birth (perhaps correct or perhaps not). Censuses provide an age (perhaps correct or perhaps not) which can be used to estimate a year of birth.