Hey, quick: what do you think a character with the uber-symbolically significant name of "Little Boy" is going to be like? If you answered: "full of childlike wonder" "open-minded" or "sweet" then good job, Shmooper. You get a gold star in symbolism.
It's through the eyes of the Little Boy that we see the changing world. It's not all roses and sunshine and rainbows through Little Boy's eyes, though: in Little Boy's sections Doctorow writes some of his starkest images, like the letter from Father in the Arctic that's translucent with "grease spots on the envelope" and smells of "dead whale" (9.2) But life can be beautiful to Little Boy as well, like when Little Boy sees the approaching car of Harry Houdini after fixing his gaze "on a blue bottle fly traversing the screen in a way that made it appear to be coming up the hill" (1.5).
But whether Little Boy is taking in the pukesome details of a greasy whale-smelling letter or watching motion pictures or a baseball game, the passages where Little Boy takes the foreground are among the most vivid and descriptive. Little Boy is able to stand back and gawk at the modern era. He takes it all in, good and bad.
There's another (weirder) side to Little Boy as well. He's a clairvoyant. And yes, we might associate "grass-stained knees" with little-boyhood more often than we do "clairvoyance," but this clairvoyance is as full of symbolism as a Semiotics textbook. That's because Little Boy symbolizes not just any old small child, but the youth and awe of the new century.
When he tells Houdini "warn the Duke" (1.6), foreshadowing Houdini's meeting with Archduke Franz Ferdinand later in the novel. How does he know this stuff? Because he's not just a little boy, he's a dang little century.
So why does Little Boy collect items and experiences—like when his Uncle discards all the silhouette portraits of Evelyn Nesbit? Why does he treasure "anything discarded" (15.1)? Shouldn't a Little Boy/New Century be laughing maniacally and saying "Out with the old, in with the new! Mwahahaha!"? Sure, but remember that the whole Evelyn Nesbit shebang happened in the 20th century. Little Boy, in his role as Little 20th Century, wants to keep all of the pieces of the 20th century intact.
Maybe this is so future readers (and writers—lookin' at you, Doctorow) can have access to all that transpired in the first decades of the mighty new century.