Note- This question was partially inspired by the civilization in Star Trek: Voyager Season 6: Episode 12 "Blink of an Eye", plot here.
You are an ordinary person, with an ordinary life, and an ordinary house. One day, you wake up and find something you weren't quite expecting. Out in your garden there appears to be a small stone age civilization. You don't seem to remember seeing them before, so you assume it just developed. This was, of course, of great interest to the world, once that idiot kid who won't leave you alone catches a glimpse.
Once the government arrives, though, something's different... they're no longer stone age. It appears they've developed a feudal system. In 2 or so hours. Remarkable! Either way, the government is here, and, in another 2 hours, so is everyone else. Oh look, there's the UN Secretary! And that's the UN High Command. You stand in a corner as Putin stalks by, and then you meet Rex Tillerson warmly (he does smell faintly of Vodka and petroleum, though). By this time, the society appears to have erected a small steam factory, and it is spoiling your Rhododendrons.
Now, with any belligerent military man comes the demand- "They could be dangerous! Kill them all!". For some reason, this receives astounding agreement, and they attempt to tear down the factory 'in the name of security'. This fails miserably as the commanders were talking fairly loudly, and the citizens caught wind.
Using their newly developed muskets, they fend off the men with a couple warning shots. The generals try again with force, but the people have learned their tactics, refined their technology. This continues, and no matter how hard the generals try, they simply cannot destroy the civilization.
Is this feasible? Can a civilization develop so rapidly? Can they adjust to, and anticipate, whatever may come their way? Can a civilization grow more rapidly than they are destroyed?