1900 census also asks foreign born for date of immigration. 1910 census has no index. 1920 also asks year of immigration and year of naturalization. 1930 and more recent census are not available due to privacy restrictions. 1865 lost in a fire.
Statistics survive, but no individual data.
1905 gives every name, age, birthplace and occupation. Index for Winnebago County only. It's always worth looking for an obituary if you have an exact date. Local obits mostly on page 4 from 1930s to about 1962 but not in a column. All obits in a column starts about 1962.