That's not really the full story. The US didn't come up with the moon goal. It was the Soviets' plan already, which is why JFK publicly announced it in a speech

That's not really the full story. The US didn't come up with the moon goal. It was the Soviets' plan already, which is why JFK publicly announced it in a speech: to force them into a public prestige battle. The Soviets had the habit of repeated private failure. If they achieved something, they'd announce it afterwards; if they failed, they kept quiet. The US broadcast launches on TV and pre-announced goals, which was a major propaganda effort and much more effective than post-flight releases.