A manned lunar landing only 12 years after the first successful launch of a satellite into Earth orbit.
Bonus points because the team that put together the moon landing didn’t even have anything to do with the first satellite.
The main reasons for this: Hollywood, after 1927 (and television, after about 1950), and the US involvement in WWII (and postwar dominance). The takeover was not only effective, but unbelievably swift.
The English language is itself something of a fluke: It was an accident of history that William the Conquerer became King of England (his claim to the throne was shaky, to say the least), bringing Norman French into contact with Anglo-Saxon. Otherwise, modern-day English speakers would have ended up with a language much more like Dutch or Frisian. This is the only case where the influence of a single individual (William) resulted in the creation of a major new language.
None of those were long shots at all.
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The Persians found pacifying border regions impossible. Not the only defeat they suffered, nor the most far reaching (those would be Indus Valley and Egypt)
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The Persian Empire in Alexander era was already past its sell-by-date. It would have lasted for a generation or two max.
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There was no chance of Hannibal marching on Rome. He did not have the ability to reduce the city by siege and he and the Romans knew that. And Hannibal spent the next decade and a half marauding around Italy, so hardly “overtime”.
Interesting, and ignorance fought.
Polynesians settling the Hawaiian islands
Plymouth Harbor settlement
Dutch settlements in general (of all places the African southern cape, Jakarta, and Manhattan)
The Oregon Trail
madsircool may be referring to the rumors that Chester A. Arthur (who became president upon the assassination of James Garfield) was born in Canada. The rumors have never been substantiated.
Not a problem 
As I understand it, the Reichstag had to change the law to allow Hitler to take power; similarly, the Constitution could be amended to allow a foreign born President.
They had to pass a so-called Enabling Act granting him emergency powers after the Reichstag was burned, but he had already been appointed Chancellor by President Hindenburg.
After the old man’s death, it was a simple matter of him merging the two offices into the post of Fuehrer.
IIRC, the Constitution forbids naturalized US citizens from becoming President. A US citizen born abroad to US parents is not considered naturalized (if that’s what Arthur’s status was).
To be precise, they were protesting a tax cut on tea (though the real issues had nothing to do with the the tax itself; it was a protest for self-government that was ahead of its time, but has been repeated many times since).
How about four middle class boys from Liverpool, England becoming the biggest musical act of their time, with their music still being popular half a century later. So unlikely that their own record company thought they’d be forgotten in a couple of years.
The real mystery was that the German Army officer class allowed Hitler to take power. To the generals, Hitler was an ignorant boor.
Would a cesarean delivery render a person ineligible for POTUS? If that was the case, Bill Clinton wouldn’t have been electable. 
AFAIK, he’s the only POTUS who came into the world that way.
Can’t recall where I heard that, but it stuck with me because it wouldn’t have been performed back then unless they almost lost both of them. Queen Elizabeth was born that way too.
They were good at following orders.
Say what you want about the Germans, but they were always big believers in a well-ordered society. The generals may not have liked Hitler, but he was in charge, and therefore they had to obey him.
This was how the Rwandan holocaust happened too, because Rwandans were raised to never question authority. Immaculee Ilibagiza describes this well in her book “Left To Tell”.
Would “The Long March” have been considered a long shot at the time? A ragtag group of men being harried across thousands of miles of inhospitable areas of China returns to become the new rulers.
Now, there were several thousand survivors in this ragtag group, and they apparently picked up a lot of support as they went along. Also, there’s China’s internal instability at the time. So maybe it wasn’t such a long shot. Someone was bound to be victorious.
I dunno… I mean, SOMEONE is going to be the most biggest musical act of all time. Was there something specifically about them that made it particularly unlikely for them?
They put him into power because he promised to (a) rebuild the country’s armed forces and (b) crush Marxism and parliamentarianism. The same reasons he was backed by the country’s leading industrialists (and a large percentage of the general electorate).
Their big mistake was in thinking they could control Hitler once he came to power. Once they had sworn a personal oath of loyalty to him after Hindenburg’s death, he had them right where he wanted them. They also lost what remaining influence they had after the Fritsch and Blomberg scandals of 1938.
Assuming that this isn’t some kind of joke, “natural born” in this case refers to being born within the borders of the US, or (as I believe) to at least one US parent abroad (like my daughter, who got her citizenship automatically from the Embassy in Moscow). It has nothing to do with the manner of your delivery.
If you’re a US citizen born abroad and 35+, you have to have lived in the States for a minimum of 14 years before you’re eligible to serve as President.
Well, Attila the Hun unified a steppe empire first, by almost 800 years, and overran a huge part of Asia and Europe, including invading the heart of the Roman Empire. Genghis did more and the polities he created lasted longer, but there was precedent when he did it. Still a longshot, but not quite such a bolt from the blue.
Horse nomads suddenly bursting our of nowhere and conquering huge tracks of land is something that would happen with surprising regularity - you had the Huns, then the Arabs, then the Seljuks, then the Mongols, then the Ottomans… and I’ve probably missed a few, too.