Dear Rei Kokkonen,
Thank you for posting your request to History Hub!
The National Archives has custody of Passenger and Crew Lists of Vessels Arriving at New York, New York 1897-1957 in the Records of the Immigration and Naturalization Service, 1787-2004 (Record Group 85). These files have been microfilmed and are located at the National Archives at Washington, DC under microfilm T715. These files have also been digitized and are available on Ancestry under the New York, U.S., Arriving Passenger and Crew Lists (including Castle Garden and Ellis Island), 1820-1957 collection.
We were able to find some results while searching for Pekka Wilhelm Kokkonen and the closest search result we found was under the name Pekka Kekonen who arrived at New York City port on October 13, 1901. It looks like this person was going to join his brother in America but the final destination is difficult to read. Misspelling of names was quite common in immigration. Entries on the manifest include information on relatives, appearance, and other personal information, so these details should help you confirm if this is the correct person.
There may be a fee for using Ancestry.com, but can be accessed for free through a NARA facility or through any participating universities or public libraries. Some information may be available for free on Family Search with the creation of an account.
As a public health precaution due to COVID-19, all National Archives research rooms nationwide, including those at Presidential Libraries, are closed to the public until further notice. Please check NARA’s web page about COVID-19 updates for the latest information. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this is helpful. Best of luck with your research!