"When everybody else is colonized/enslaved/segregated/not allowed to be educated by you..., your scientific discoveries tend to progress faster."
I think the way to avoid this "impression" is to provide an accurate historical account as to how Europeans scientific discoveries came into dominance and provide examples of scientific discovery made by non-white or non-Europeans scientists.
As mentioned in the comment by Obie 2.0, during the pre-colonial period, discoveries in medicine and mathematics were more advanced in the Arab world, and many key results were independently discovered in India and China. For example, many modern mathematicians have ancestry with Arab mathematicians such as Ibn al-Haytham (even though many will usually claim a better-known, white European man such as Gauss or Laplace as their ancestor). As another example, the Pascal triangle was discovered and documented centuries before Pascal.
The rise of European science was intimately linked with colonialism. Again using the math genealogy example, there is a clear surge in the number of descendants by mathematicians in the 18th, 19th and the early 20th century, at the heights of European colonialism, during which over 90% of the continent were directly affected by European colonialism. The whole continent of Africa, Australia, the Americas, India and various parts of China were directly under European control, and it has largely remained this way. I think it is pretty easy to imagine why, for instance, no famous Native American or African mathematician emerged during this time, and in the centuries after. By the way, much of these technological discoveries were used for things like warfare, espionage, surveillance, social control, resource extraction, deforestation, etc., instead of humanitarian purposes.
This, however, does not preclude significant modern discoveries made by non-white or non-European scientists. They can be found everywhere, particularly in mathematics and medicine. A recent article in my field mentions https://en.wikipedia.org/wiki/Tu_Youyou, whose discovery saved millions of lives. Just because she is not mentioned as much as Alan Turing or William Shockley doesn't render her work any less important and groundbreaking.
It should be clear now, even with this brief exposition, why European scientific discoveries dominates how we think about scientific discoveries. Does it make sense to only mention the achievements, while simultaneously hide the reason as to why those achievements were made by a particular subset of people?
For a modern example, sure, Steve Wozniak "the Woz" made great discoveries in the field of computer hardware, but this is during the time black people cannot go to school, so is it really surprising that a white European male made those discoveries instead of other people? It seems to be that we are not being intellectually honest when uttering the phrase "all modern science was discovered by the white man".
As a multilingual person, I know that many discoveries by French and German scientists are not well publicized in the Anglophone community, I regularly edit WIkipedia articles of dead links of non-English European scientists and mathematicians. I can only imagine how poorly represented are people of color in the Western, English-speaking spheres.
To avoid European bias in teaching, we must clearly address the European bias in how history is presented.