An electronically readable international passport is required to travel to the USA. You passport has to be valid during your entire stay. Also children and babies need a passport.
Apply for a passport in time, because it can take several weeks for your passport to be issued. In several countries you can opt for an emergency procedure, but this will come at a high cost. You need to have your passport before you can apply for a visa or ESTA. (Check here if you need a visa or ESTA.)