From what Jack said, it wasn't easy to see it.
JACK: Oh really? Did you know that minutes after dusk, when the sun is just right you can see Sputnik with the naked eye. Maybe tomorrow I could show you.
But he was
a sharp kid you know.
He was, and Sputnik wasn't easy to see during the few months that it was in orbit. You had to know where to look, and many people --- then and since --- have sloppily assumed that it couldn't be seen. But, per the National Geographic
article about the launch of Sputnik (I don't have the issue on hand, but it would have a cover date of around January 1958, and can be found in every used book store ever), observers could and did see it with the naked eye.
(Confounding things is that the upper stage of the rocket which launched Sputnik also orbited for a good while, and as a much larger object was
more easily visible. People seeing just something shiny moving in the night sky would, reasonably, think they had seen the satellite when they were actually seeing the rocket stage's shell, and this probably helps confound the matter of naked-eye observations of Sputnik 1.)