The local library may have copies of old city directories produced my the municipality.
The 1900 through 1930 censuses lists the individual's year of immigration to the United States. Don't be surprised if they are all different dates.
The "Social Security Death Index" is an online searchable database. It only includes the names of deceased individuals whose deaths were reported to Social Security. Beginning in 2014, rules governing the "Social Security Death Index" changed. Records for the most recent 3 years are not available.
A time line begins with your ancestor's birth and is filled in with various events in his life. Continue to fill this in as information becomes available to provide a picture of your ancestor's life. Several of the genealogy software programs assist you with this.
The National Archives and Records Administration (NARA) in Washington, DC and its Regional Branches, is the principal repository for records relating to the US federal government. These include the original paper copies of the federal census, all pre-World War I military records, Native American records, military service and pension records, naturalization records, ship passenger lists, land-entry case files, and homestead and bounty land warrant records. NARA's website is the place to begin research for federal records.