The US seems to be somewhat unusual for a former colony since it just like 100-150 years after its independence had surpassed pretty much all European great Powers in economic and technological development. It is not clear to me how US managed to do such enormous growth so quickly, did it simply get alot of things right from the start that others did not?
Many of the above points are valid and possibly the most important factors.
Some things that haven't been mentioned yet but certainly played a part:
1.
The US was full of white people during an era when the moneyed classes were unquestionably racist. It had experience with well-respected autonomous government where other colonies ended up under some combination of utterly contemptuous foreign rule, continuation of corrupt local rule, and being intentionally set up to fail, as with India's Muslim/Hindu divides or with the borders in Africa and the Middle East being drawn with nearly complete disregard to the local populations.
Another factor of this is that (until relatively recently)
the US deeply felt that the Enlightenment, the Rights of Man, and the Common Law were its own heritage and embraced them wholeheartedly, whereas many former colonies see them as something thrust in from the outside that need to be repudiated or, at least, leavened with indigenous religion, paternalism, aristocratic classes determined by birth, &c. It's understandable but mostly detrimental to those other countries.
2. Partially from the above and partially from its legitimate commitment to Enlightenment ideals,
the usual rule of law in the US was very attractive to foreign direct investment, particularly the English and Dutch. The most important of America's banks and railroads were owned and controled by foreign powers for decades and the investment bubbles following the collapse of canals or this or that set of railroad booms tended to wipe out more foreign investors than local ones.
3.
It had an utterly charmed economic path. The US had
Alexander Hamilton to steer a course through its early money trouble, and he had Washington to protect his work from populist opposition. The land speculation most of the upper class was obsessed with early on was ultimately beneficial for developing the interior, and
a continent's worth of cheap, healthful land kept fertility high for decades on top of the immigrant arrivals. The merchant houses in the NE that had depended on the triangular trade were able to switch over to
whaling and then the Chinese market opened by Britain for its own reasons. Even when Andrew Jackson fought the Bank of the US intended to better protect foreign investment and the upper class, he was also willing to beat up South Carolina over their resistance to the tarriffs that paid for his army and government. The South's
cotton was white gold for the planters and the federal coffers, which is why they thought they could survive on their own and why the North absolutely refused to let them go. It was dependant on open international trade, but
the British were underwriting that with their navy and free trade policy for their own reasons. There was plenty of actual
gold in California, as there had previously been in Carolina & Georgia and would later be in Nevada & other western states. By the time those ran dry and the Civil War and British planting in Egypt and India and the bole weevil cratered the cotton market, protectionist policies and corporatist favoritism by local political machines had built a powerful industrial machine. The timing of the US buildup matched
the second (electrical) industrial revolution and allowed its new factories to be much more productive than those in Britain. By the time
that was starting to putter out, the US turned out to have the largest and most easily accessed
petroleum deposits then known. Europe was committing geopolitical suicide in the World Wars, which bought everything the US could produce, left
the dollar the king of international currency just as everything went fiat, left the US in ownership of its own industries and infrastructure, and drove federal investment into the new high-end sectors (
automotive and aerospace industry,
microelectronics, computers, &c.) that have dominated commerce since. Even DARPA's toss-off nuclear-resistant communication network ended up transforming international society as
the internet, which left the US long in control of its standards and flagship companies.
If you compare the US to other former colonies, you'll see some foundering at every single stage of each of those economic and financial transitions.
4. You'll notice some important parts of that economic history involved
the US's protectionism and investment in its own industry. That was important to protect it from the bigger fish until the US had become its own whale; by that point, the US had the clout to reshape international commerce in a
less protective direction
further enriching itself.
5. Another major factor that Ming alluded to is that
the US mostly has a very healthful climate. This doesn't just mean it's like Europe and less likely to kill Europeans than Africa was. Africa has dozens of endemic diseases that grew up alongside humanity and our cousins that still continue to wreck life for people there. China and the US periodically end up with epidemics from trade, their markets, and our factory farms but mostly we live our day to day life without everything in the environment trying to introduce parasites. Africa has lots of governmental, sectarian, and educational issues but, if the Gates Foundation & others can really make a dint in its endemic diseases, life will still unquestionably improve for millions regardless of their former status as colonies.