Higher labour productivity appears to have been an important cause, probably due to both higher wages and more inclusive social institutions for much of the US population relative to the UK's. The higher wages were because of the high ratio of land to labour. The more inclusive institutions can be illustrated by higher rates of education. Allen (2015) notes that:

In 1880, for instance, 90 percent of school aged children in the United 

States were enrolled in schools in contrast to only 55 percent in 

England and Wales (page 325). 

The popularity of public education in the US may have been in part due to business owners facing a work force drawn from a variety of backgrounds due to the high rate of immigration. 

The US also had (has) significant natural resources, though American manufacturers typically paid similar or higher prices than the British due to tariffs. US and Canadian governments invested in transport infrastructure that helped make these resources widely available internally. 

Another, more disputed, cause is American domestic tariff protection of manufacturing in the 19th century, combined with its large and growing domestic market. More disputed because there's plenty of countries that have tried tariffs to grow domestic industry without success, including my own NZ. But Allen argues that the 19th century US was in an unusual situation with its large and rapidly growing internal market, large both in terms of numbers and wages. The sheer size meant returns to scale for manufacturers, the growth meant lots of opportunities for them to learn from doing - Allen points to changes in the layout of blast furnaces (for iron) and steel mills. These could offset the downsides of the tariffs in the form of higher input prices for American manufacturers and consumers. 

I'll add that the issue of a 'headstart' in economic development isn't that important, as illustrated by the rapid post-WWII growth of countries like Italy and South Korea. Physical capital is always depreciating, even a building's economic life is only some 60 years or so - I speak as someone who has recently had to replace my home's roof. Engines, trains, bridges, all require ongoing maintenance or replacement in any rich country. Intellectually too, new generations arrive and need educating.  The difference between a developed country and a developing one isn't that profound from this view point: perhaps the developed one does more maintenance and less new builds. There's even people who argue that one reason countries like Italy and West Germany were performing better than Britain in the first decades after WWII was that they'd had so much infrastructure destroyed that they were reaping the benefits of putting in new technology. I don't believe that - the US was doing better than the UK then too. But the argument does illustrate that headstarts aren't automatically an advantage. 

In short, the US benefited from higher wages, a more educated workforce and arguably was in a sweet spot with manufacturing tariffs given its large internal market. 

Sources

Robert Allen (2014) “American Exceptionalism as a Problem in Global History, The Journal of Economic History, Volume 74.

Pieter Woltjer (2015) Taking over: a new appraisal of the Anglo-American productivity gap and the nature of American economic leadership ca. 1910, Scandinavian Economic History Review, 63:3, 280-301, DOI: 10.1080/03585522.2015.1034766