So this is an interesting question, and one that we don't typically answer here on this community because we don't tend to answer speculative scenarios. However, it is worth answering a question which is quite similar to this question, which is, "did the British try to avoid or stall the American Revolution?" And this is one I will be happy to answer. I'd also throw out a disclaimer that part of my answer will also be taken from two entrie on my website that I wrote up not long ago, that you can check out here. The short answer is, no they never tried to do that. But the "why" they didn't try is a bit more complicated, which I will explain below.
Answer The American Revolution was arguably a pretty big shock to the the British Empire. Heading into 1770, it was barely an imaginable thought that any type of organized resistance could take shape in one or several of His Majesty's colonies. Sure smaller uprisings had taken place, like Bacon's Rebellion a century earlier, but those were always loosely organized and never represented any group the size of a colony. Nor had the colonies ever been united together until the middle of the century-- many colonies still squabbled over minor things like their borders on the frontier even after the Revolution was over! It wasn't until the early parts of the French and Indian War that any national figures even began talking about the North American colonies standing together. In 1754, just as the war broke out, the very notion of being united against an enemy was not something that was easily embraced and it worried many American leaders. Ben Franklin drew his well-known political cartoon of the snake with the words Join or Die printed on it, which encouraged colonies to see themselves as a united entity, or risk losing everything to the French or Native Americans.
So by the time the 1760s rolled around, the idea of working together as united colonies was already a somewhat established concept. Across the colonies, protests (both passive and active) shook the nation, and I don't think Great Britain was quite ready for it. They were especially not ready for the fallout that followed in the early 1770s in New England which culminated in the Boston Tea Party. Most people are at least vaguely familiar with the story, but a refresher is easy. Following a series of oppressive tax acts imposed on the colonies in the 1760s, the colonists banded together and fought off the taxes. Tea was the only major import that still held a tax for the colonists heading into the 1770s, which they generally were okay with and accepted it. But in 1773, the New Tea Act saw to give the giant cooperation, the British East India company a benefit of having that tax lifted against their tea, thus giving them a significant advantage in the market. The colonists were irate. American colonists hated corporations at this time, especially the Bank of England and the British East India Company, so any advantages to them was enough to spark unrest. That's why in December of 1773, colonists in Boston boarded an East India Company trading ship which was filled with tea, and dumped it all over-board. And when the British responded with increased military force, other colonists across America started doing the same thing. Pennsylvania, Maryland, South Carolina and most other states all had their own "tea parties" shortly there after, in a move of solidarity with their northern brethren.
It is widely believed by most historians of this era that the British were, at least in some way, were not expecting the colonists to unite as they had planned to. They had no army. They had very little money (America was struggling through a depression during the previous decade) and they would have to rely on militia's (so it was believed) if they did go to war. So the British ignored the pleas from the Continental Congress and instead tried to tighten their gripe. What they also weren't prepared for were any American victories, which the American military did have several during 1775 before their periods of immense failure in 1776. But by then it was too late. The colonists -- especially sizable portions of the over-all population in the middle and northern states -- were very much dedicated to the concept of separation from the British crown by 1776. Within the next two years, when Britain realized that this war with America would be incredibly expensive, they did try to end the war with an offer of representation in Parliament and a few other perks, but it was, of course, quickly rejected. Had the British government made a similar offer three or four years prior, perhaps the gentry would have accepted it -- but who knows really. All we know is that by the time the British government tried to avoid war, it was already far too late.
Lexington and Concord in 1775 was the first real engagement between the colonists and the British. The fighting here was not extremely bad, and the colonists even tried to make peace with the British by sending the Olive Branch petition. Even though Parliament received it, the Petition only arrived after the events at Breeds Hill. The Battle of Bunker Hill was definitely an act of war on the colonists part with a result of over 1,000 British either wounded or killed. This is when the British really understood that the colonies mean real business and started sending a significant number of troops over.