Early is a relative term. Its meaning is vastly different from one context to another. As a qualifier in connection with “morning,” the word’s meaning is innocuous. “Early Man,” on the other hand, carries more gravitas.
But then, consider this.
This topic seems more important to me now because this morning I am leaving the house at 3:45 a.m. to take my wife’s friend to the airport. In this context, and considering that my sleep the night before did not last more than two hours, “early morning” seems to have almost as much gravitas as “early Man.” Possibly more.