First, I'm assuming that by "much" you mean "primarily driven by."

Second, when discussing the US "untouched-ness" versus European "bombed out-ness", it's better to look at the relative share each held of world manufacturing, rather than simply the share of European capital wrecked by the war.

To understand the basis for the Post-War Boom, you first have to understand that pre-war, the United States was under-performing its potential. No nation was hit harder and longer by the Great Depression. In 1929, The US accounted for 43.3% of all world manufacturing; after the double-dip recession in 1937, it only accounted for 28.7% in 1938. [1] To give some perspective, in car manufacturing, as much as 50% of capacity was unused when Pearl Harbor happened. [2] Even with this however, the US remains the world's largest economy. Keep that in mind; the US economy is a massive and, importantly, largely self-sufficient beast.

The war finally utilized all that ridiculous potential being held back by the Depression. This is where the US being "untouched" across an ocean helps; not only did the war finally put a sputtering economy back into gear, but none of that growth was lost to bombing or other damage. To add to this, with so much under-utilization, the US economy can also simultaneously afford an increase in the demand and production of regular, non-war goods rather than converting such factories to war production, as people with new jobs in war industries can finally afford them after years of hardship. [3]

So now when the war ends, the US has an economy which is finally running at full potential after years of crippling unemployment and under-investment, and with investment and demand for consumer goods back where they would have been without the Depression, and then some, job opportunities to produce those goods were back. Also returning are millions of young men who have spent the last four years in the Pacific and Europe. Many of these men will also go to college through the GI Bill, and thus eventually get higher paying jobs than they would have without the war, further stimulating demand as the Boom years continue. [4]

So in the immediate aftermath of the war, you have an economy that is not only bursting with demand previously suppressed by the worst economic crisis in history, but a labor market bursting with young men to meet that demand. And since it is largely self-sufficient in resources, it can build on all this regardless of the capacity of the rest of the world.

What is important about the destruction, and especially UK debt, wrought upon the rest of the world is the relative economic dominance it afforded the United States. It now accounted for half of world manufacturing and 42% of income. [5] With this, the US became the undisputed center of the world economy, a process that had been long in the making, but was accelerated and strengthened immensely by the war. Instead of a gradual move to the top and shift from Pound Sterling, the US Dollar was catapulted up and Sterling plummeted downward. What would have been a good-to-great Post-War Boom with an economy that had finally shook off the Depression became an amazing Post-War Boom with a world economy dependent on it.

TL;DR: The Boom itself wasn't primarily driven by the demand for US goods in ruined European countries, but by a domestic economy that was, with the re-entry of millions of working age men into the work-force, building on the war's ending of the Great Depression. However, the United States' relative economic dominance did add on to the Boom.

[1] - Kennedy, Paul, The Rise and Fall of the Great Powers, (New York, 2013) 330

[2] - Kennedy, David M., Freedom From Fear: The American People in Depression and War, 1929-1945, (New York, 1999) 617

[3] - Kennedy, Paul, The Rise and Fall of the Great Powers, (New York, 2013) 357-8

[4] - Over 100,000 more men received degrees in 1949-50 than men and women put together in 1939-40. Patterson, James T., Grand Expectations: The United States, 1945-1974, (Oxford, 1997) 68

[5] - Patterson, James T., Grand Expectations: The United States, 1945-1974, (Oxford, 1997) 61

Sources

Darwin, John, Unfinished Empire: The Global Expansion of Britain, (London, 2013)

Kennedy, David M., Freedom From Fear: The American People in Depression and War, 1929-1945, (New York, 1999)

Kennedy, Paul, The Rise and Fall of the Great Powers, (New York, 2013)

Patterson, James T., Grand Expectations: The United States, 1945-1974, (Oxford, 1997)

There are a lot of theories about why there was such sustained growth, not just in the USA but globally during the 1950s and 60s, and given that we are talking about only one time period it's not possible to prove any one. It's possible that multiple ones are true.

That said, it seems unlikely that it was down to rebuilding Europe's manufacturing base. You don't explain the intermediate steps in the hypothesis you present, but often these are cases of what economists describe as the broken window fallacy, from Bastiat in the 1840s. Basically yes there was a lot of economic activity replacing manufacturing capacity lost to WWII but if there hadn't been a war there would have been a lot of manufacturing capacity that was available to make things that would have actually improved people's lives rather than destroying them.

But without knowing the chain of logic behind the hypothesis you present I don't know if it commits this fault. Amongst other points, there's a distinction between measured economic activity and human utility: perhaps if WWII had never happened people would have taken more holidays rather than working long hours to rebuild Europe and thus WWII increased measured GDP, even though it decreased utility.