I would recommend The Rise and Fall of Great Powers - Paul Kennedy. In the opening chapter of the book he analyses the great early civilisations (Mongol/Shogun Japan/Ming China, etc) and compares them with their European counterpart before concluding that Europe possessed multiple benefits which culminated in its head start in dominating and the 'rise of the West', these are:

• The geography, which was not conducive to rapid mass invasion unlike the Russian steppes to the East and therefore fostered decentralised power - "a political map of Europe drawn any time after the fall of Rome [would] look like a patchwork quilt".
• The diverse climate and farming conditions which encouraged the production of diverse products, thereby improving the chances of exchange within the continent and the use of Europe's many navigatable rivers to transport such goods creating an active merchant class. In particular, Kennedy points to the nature of trade in goods such as wool and timber being more beneficial to a prospering civilisation than the Eastern speciality in luxury goods.
• The surrounding seas (Mediterranean/Baltic/Black) furthered international trade and lead to a stronger shipbuilding industry than found elsewhere. The international trade also stimulated a modern financial services industry much faster than contemporary rivals with the introduction of banking and bills of exchange.
• The close proximity of multiple warring nations was said to have encouraged constant military innovation and a rapid evolution of warfare tactics. This delicate balance of power was maintained in part because of the prevalence of mercenaries fighting for the highest bidder and technological parity. These factors, when introduced to a more insular civilisation with no need to innovate to compete locally can be used to explain European conquest in other regions.
• Finally, Kennedy makes reference to the increasing willingness of feudal lords and rulers to tax trade at an appropriate level so that both the trader and state have a vested interest in the continued movement of goods and later on, into expanding into new territories in the New World. This market-based approach was said to be one of the most influential reasons and one which differentiated Europe from other civilisations of the era. The examples cited were Japan under Tokugawa rule and dynastic China both of which employed isolationist foreign policy to a degree.

I don't know that there is a consensus, and I think the discussion continues today. There was a very recent interview with Turkish Economist Dani Rodrik where Rodrik was asked why Turkey didn't develop like western Europe. His response, referencing Barrington Moore, had a lot to do with the structure of the agricultural system. His reasoning was, in part, because Turkey and Western Europe started with the same basic agricultural economies and went in different directions. Western Europe had smaller peasant land holders while Turkey had larger landlords. He then said that Turkish agricultural processes were more labor-repressive than, say, Britains. This lessened the impetus to diversify into industry.

He then talked about the importance of spreading ideas within western Europe, positing that if France's initial conditions were more like Turkey's, and if France had been further east its outcomes would have been very different.

I'm not sure what other historians think of this train of thought; Rodrik may be considered in part an economic historian, but most of his work has to do with more contemporary issues in economics. Anyway, this isn't even really an answer to the question, as it doesn't really get into the rise over a short period issue.

Source: "A Conversation with Dani Rodrik" on the website medium.com and hosted by Tyler Cowen: https://medium.com/conversations-with-tyler/a-conversation-with-dani-rodrik-e02cf8784b9d