The notion that the colonists were able to best the British army with their own resources and skill is very old. I have a theory myself that some of it came from the recollections of the Continental soldiers who survived into old age. As Washington generally avoided decisive battles after 1776, most ( like Joseph Plum Martin) would have recalled poor food but no awful defeats, and the political leaders who had actually borrowed and bought supplies from overseas ( like Robert Morris) were long dead and couldn't dispute them. The idea of Cincinnatus - the farmer who stops plowing and quickly wins a battle, then returns to plowing- has always been popular. But there's never been any doubt among historians about the question of whether the Americans did it alone.

The colonies had been set up very much as producers of raw materials, with the expectation that things like tobacco, rice, wheat, indigo, codfish, and timber would go to England and pay for hats, shoes, belt buckles. The economy was agrarian, manufacturing was minimal. By 1776, craftsmen had become more common ( immigrants discovered they had a better market and no guild regulations than at home) . There were a good number of guns- the surviving ones indicate a large number of gunsmiths (and farmers have always tended to be good customers for gunsmiths). However, only about 1/3 of the guns in the colonies were made there: the rest were imported. And even the ones that were made in the colonies almost always had imported locks. There were also not nearly enough military muskets. The state militias were not well-equipped: the Williamsburg Armory in 1775 had only 527 old muskets and 180 new ones. Mostly there were sporting arms: rifles ( especially in the new frontier areas of Pennsylvanian, Virginia, North Carolina) and fowlers ( shotguns, in New York and New England , where there was less large game). When von Steuben looked at the army at Valley Forge, in 1778, he he was amazed to find a variety of rifles, carbines, fowlers, and muskets could be found even within one company- with a variety of calibers and ammunition.

There was also little to no gunpowder manufacturing. When Israel Putnam said "don't shoot until you see the whites of their eyes" at Breed's Hill, he was likely thinking less about tactics and more about not wasting gunpowder, making every shot count. The revolt in Boston managed to stockpile 80,000 pounds, but it was nor nearly enough.

The colonists themselves knew immediately that they needed help. Silas Deane and Arthur Lee began negotiating with the French on behalf of the Continental Congress even in 1775, and with the assistance of Beaumarchais was able to get a million livres worth of guns, gunpowder, cannon, cannonballs, gunflints and materiél like clothes, uniforms, sails, tents, etc. sent over in six boatloads. The French ( and the Dutch) would eventually supply the rebels with around 1,500,000 pounds of powder, and ingredients ( mostly saltpeter and sulfur) to make another 700,000 pounds. The French supplied as well at least 102,000 military arms, mostly muskets, the Dutch at least 2,100. Perhaps the biggest indicator of how much the colonists depended on foreign help is by their war debt: about $13,000,000. And that was just what the colonists owed: that does not count the cost for the timely intervention of the French navy , especially at Yorktown. The price for the French was much higher.

The colonists would try to make some of their own arms. But it was a very difficult task. There were no gunfounders to make cannon. As I said, their gunsmiths had greatly depended on imported locks- almost entirely from English makers- and those quickly became unavailable.. There was also a problem of security: the colonists could seldom hold ground against the British army, and Colonial armories were a very important target . The Rappahanock Forge complained bitterly of not being able to get supplies and losing its employees to recruitment by the army until 1781, when the approach of Banastre Tarleton's cavalry forced the gunmakers to grab all the tools and flee just before the shop was destroyed.

We can conjecture, get into counterfactual arguments, and claim that, given time, the small British forces , trying to operate in a vast , sparsely-settled landscape, would never have been able to ever subdue the rebellious colonies, even without foreign aid. That Washington would have still outlasted them in that case is maybe possible. Certainly, the British had other military commitments: they had been at war for most all of the 18th c., and were beginning their colonization of India. But we can also compare the 1776 revolt to the Seven Years War of only a couple decades earlier: That had started out as a war of French soldiers and their Indian allies vs the colonies, and the colonial militias proved to not be up to the task: the government finally had to bring over British professional soldiers. And the colonies had also been divided in their response to the French in the Seven Years War: it's also possible that after some years of misery and destruction they would have also divided and individually bargained with the British.

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M.L. Brown : Firearms in Colonial America