It is a bit of an odd phrase, I can see why it would be confusing. Earliest is the superlative form of early. Early is a comparative statement, meaning that it occurred near the beginning of something (in this case the 20th Century, e.g. 1920s). Earliest means the "most" early that it could be. It implies a time in the very early 20th Century, for example 1900. It is almost a poetic way of talking about the beginning of the century. It is confusing because you can't have more than one 20th Century to compare. It just means the very beginning of the 20th Century, the earliest time in that century that you could be talking about.

I think very few if any native English speakers would refer to "the earliest 20th century". That would imply there was more than one 20th century.

You can use it as a Adverb or a adjective. ( adjective ) At or near the beginning of a period of time or course of events or before the usual or expected time. "early morning"; "an early warning"; "early diagnosis"; "an early death"; "took early retirement"; "an early spring"; "early varieties of peas and tomatoes mature before most standard varieties" ( adverb ) Before the usual time or the time expected "she graduated early"

"the early 20th century" simply means a time near the beginning of that century. I don't think I would say "the earliest 20th century," because that doesn't make much sense. I would say "in the earliest part of the 20th century" which would mean the very beginning of it.