Story identification: Stranded alien ship builds Earth civilization to help it fix the spaceship

Question

I'm trying to figure out the name of a sci-fi short story I read a while back. Hours of Googling were no help. Can anyone figure this out?

The punchline of the story is that all of humanity was created for the purpose of providing a missing tool which is required to fix a broken alien spaceship was stranded somewhere in the solar system (Jupiter?). In the end, a child with a toy, which turns out to be the requisite tool, stumbles into a spaceship launched to that planet, and it all turns out to have been designed by the aliens to get them their missing tool, so that they can fly back home.

Answer 1

The Sirens of Titan by Kurt Vonnegut Jr. has many of the plot points that you remember.
The novel includes the revelation that humanity had been secretly manipulated for millennia for the purpose of repairing a stranded space ship. The child of one of the main characters repairs the ship; he uses not a toy but a small piece of metal that was picked up randomly.

Check out the Wikipedia page for The Sirens of Titan.