Dear Iryna Bodak,
Thank you for posting your question to history hub.
The United States Government does not ordinarily create or maintain birth, adoption, death, marriage or divorce records. Such records are made and kept by State and local governments rather than the National Archives. We suggest that you continue searching substitute record sources such as probate records, church records, and newspaper records that may uncover more information about your grandfather. Since your grandfather was born in another country and then moved to the U.S., you would need to begin your search in his country of birth.
Another great resource for you to find information about your grandfather would be researching Immigration and Naturalization Records held in the National Archives. A guide to those records can be found here: https://www.archives.gov/research/immigration.
The vast majority of records in our collection are not name-searchable. For more information on conducting genealogical research within our records, please visit our webpage: https://www.archives.gov/research/genealogy.
For the years that you know your grandfather lived in the U.S., the Census is a great resource for verifying where an individual lived who they ,lived with, and their country of birth. Learn more about census records and how to access them here: https://www.archives.gov/research/genealogy/census/about
We suggest that you review the FamilySearch Research wiki page for the state(s) in which your grandfather was known to have resided https://www.familysearch.org/wiki/en/Main_Page.
We hope this information is helpful in your research!