Greetings from South Africa, I have Czech ancestry and some knowledge of their records (which are in general well kept, very detailed and becoming digitized and more accessible from year to year).
However, you need to know the TOWN of birth in Bohemia of your ancestor, as European records, unlike England from 1837, have no nation wide, alphabetical index to births, marriages and deaths, records were kept on a local basis. I see him in the US Federal census from 1900 which of course, only furnish country of birth and of parents. Naturalization papers, passenger lists on arrival, tombstones, cemetery records, obituaries and of course birth, marriage and death certificates could give you a town of birth. If he was in the Austro Hungarian army, the surviving Czech records are excellent, alphabetically arranged, and which furnish year and town of birth, occupation, physical description and service record and other data, they are known as Grundbuchblatter and are at Familysearch and other sites.
Good luck with research and if I can assist further let me know.
Kind regards from South Africa, Naartjie + them fur angel BEASTS.