Something that Charles Murray's 2003 book Human Accomplishment made clear was that most of the world's major civilizations outside of Europe were in cultural stasis or decline by 1500, before the arrival of Europeans. If you ask Chinese, Indian, or Arab scholars to list the most important scientists and artists in their history, their lists start to peter out over the last millennium. This is rather like how the ancient Classical world's accomplishments start to slow down after the peak in the 400s BC. The New World's accomplishments seem to have peaked with the Mayans, who invented writing, but then started to lose it.
As a conservative, I have to be admit that these trends tend to be due to conservatism: reverence for past accomplishments and satisfaction with the current life start to undermine the hunger for new achievements. (The Ancient Egyptians were the first to illustrate this tendency, making rapid progress about five millennia ago, then being mostly content to maintain their high relative level of civilization for thousands of years until Alexander's conquest.)
The main exception to this pattern of stasis outside of Europe was Japan. In 1601, Japan began a policy of isolationism, which lasted for 250 years. During this period, Japanese cultural accomplishments continued steadily. To take one example, the tracking of sports statistics, a minor but telling aspect of modernity, seems to go back to late 18th Century sumo wrestling. Similarly, the most famous Japanese picture in the world today, Hokusai's The Great Wave off Kanagawa, is from around 1830. So, Japan was continuing what looks like steady progress in a world in which backsliding was the norm. Thus, when the West rudely intruded in 1853, Japan was able to modernize itself with remarkable speed, avoiding Western conquest until the development of the atomic bomb.
Japan in 1601-1852, however, was not taking off, accelerating, the way Europe did, with Britain increasingly in the lead, especially with the Industrial Revolution. Japan was much farther behind the West in 1852 than in 1601.
Interestingly, Japan's geographical position off the coast of East Asia is rather similar to the British Isles' favorable position off the coast of Western Europe. If we assume the English (like their offspring in the New World) benefited enormously from the island privilege, what Shakespeare hailed as:
This fortress built by Nature for herself Against infection and the hand of warJapan, then, was the most likely place outside Europe for the right combination to come together for humanity to break free from the Malthusian Trap.
So, without the West, would Japan have yet achieved science and the Industrial Revolution?