Another "of course, why didn't I see that?!" symbol: that ball in stanza 23:
Oh, the places you'll go! There is fun to be done!
There are points to be scored. There are games to be won.
And the magical things you can do with that ball
will make you the winning-est winner of all. (23)
Yes, we're talking about a real ball used for the game of… whatever game Seuss is depicting in this picture. But we're also talking about success itself. If only we could boil success down into one ball in real life, we'd all be set.