Let’s say you found an old book dating back to 1872, for example.  The book is big, old, and contains data pertaining to immigrants arriving onboard ships at ports along the Eastern Seaboard of the United States.  You know enough that this book. . .

definitely is in the Public Domain in the U.S. (published before [...]

Public Domain consists of works that are not protected by copyright law.  That is what defines Public Domain.  No permission to use is required from the copyright holders, if they were copyright holders in the first place.
Some works were never copyrighted when originally produced.  Think of all the free software we can simply download and [...]

First – What is the “Public Domain”
The Public Domain refers to the huge and diverse compilation of creative works that are not under the protection of copyright law.  Artisitic creative works include films and plays, paintings, photographs, drawings, illustrations, cartoons, postcards, to name some examples.   Literary and musical examples include books, magazines, articles, instruction manuals, [...]