The narrator in Childhood's End is not a part of the story itself. He/she/the Overlord/whatever is an outsider looking into the events of the story and describing them to us, like a radio announcer calling a play-by-play in a baseball game but not playing the game itself. The narrator is also omniscient, which we know because he/she/etc. hops into the perspectives of any character or time period that suits the story. For instance:
[Salomon] had been born in Israel, the last independent nation ever to come into existence—and, therefore, the shortest lived. The end of national sovereignty had been felt here perhaps more bitterly than anywhere else, for it is hard to lose a dream which one has just achieved after centuries of striving. (15.46)
There are a couple things we should take away from that example. First, just a few paragraphs earlier, the narrator was discussing George and Jean's tour of Athens before leaping back in time to discuss the end of the nation of Israel and the birth of the artistic-centered colony.
Second, the narrator uses the word here, suggesting he actually went back to that time period or is looking at it directly (as if through a Overlord view screen or a crystal ball or some such). He not considering it abstractly, or else he would have used the word here.
Last, the narrator is able to provide us the feelings of the people of Israel—"hard to lose a dream"—and then the personal thoughts of Salomon in the very next paragraph.
So, yeah, everything points to third-person omniscient. But the question remains, who or what is it?
The entire human race has been wiped out by the end of the novel, so where could this future historian telling us this tale possibly have come from? Is it one of the Overlords? A part of the Overmind? Another alien race entirely?
The novel provides tiny clues but nothing conclusive. So, allow us to ask a question of you: What do you think?