The years when most leading powers and technologically advanced cultures were Europeans.
For sure since around 1500 until now, and during most of the Roman golden age.
Also possibly in the period between the Crusades and the Mongol Invasion, in which some of the world's leading civilizations were European.
1) Roman Empire was prospering in the similar time as Parthian Empire, Mauryan/Gupta Empire and Qin/Han Empire

2)
You know how world GDP looked like for most of history?
60 - 70% of global GDP was India + China
5 - 10% - Europe
<5% - Korea and Japan
<5% - South Eastern Asia
<<5% - modern Latin America
most of the rest - modern Muslim World
<negligible GDP of Oceania, most of Americas, most of Africa and Central Asia>
This changed in the late 18th century.
India had ~20 - 25% of the world economy before British colonisation, later it fell to 2 - 4%, you see the results today

3) In medieval times Europe was... Well, not some kind of Third World but it was certainly much less developed than Muslim World/India/China. The only 'world leading civilization' from Europe in this period was maaaaybe France but even this is far - fetched. The main powers were Muslim and Central Asian empires + China. Also in this time African empires (Mali, Ghana, Ethiopia) were not really much behind Europe.
What European dominance? You mean the brief two hundred years which is now rapidly coming to an end?
Well, yeah these were two hundreds years of European domination which reshaped the entire humanity via globalisation and industrial revolution

Generally - greatly simplyfying - you could say human history goes:
1) Birth and 'childhood' of homo sapiens - Africa
2) First civilisations - Asia
3) Key to the Industrialisation - Americas
4) Industrialisation - Europe

2 - Egypt is culturally way more Middle Eastern than African [generally speaking, people of North Africa even today feel very different from Subsaharan Africa - personally I would even say we should adopt two separate names for these two 'continents' if Europe is separated from Eurasia only for historical reasons]. Mesopotamia, India, China, all main religions => Asia
3 - I mean resources taken by European invaders [mainly silver and gold -> entire world economy reshaped], but also Amerindian knowledge and crops - currently 2/3 of all world crops originate from America; it is hard for me to imagine merchant society -> capitalism -> industrialisation without the anomaly of European Colonisation.
As I see it, radicalism is much more of a problem here than any kind of Eurocentrism.
Some intelligent people in CFC historical discussions relate to every pre-civilized north Asian tribe as equal to European medieval duchies and kingdoms.
Huh? Never encountered something like that.
What is truly radical and as stupid as Eurocentrism is Afrocentrism. According to Afrocentrism:
- Egypt was black civilisation
- ...and Greek philosophy was based on Egyptian philosophy so -> 'African philosophy' is dominating in the world

- ...well, generally many Greek philosophers were apparently black

- ...hey, guess where did Jews come from according to Afrocentrism?

- including Jesus
- also hella lot of great historical figures were in fact black: at least one Roman emperor
- my favourite statement was that medieval English king was African because he was called 'Black'


- Mali Empire reshaped the entire world economy
- generally speaking 'African resources were used to built the modern world = credit should go to Africans'
- African states were very advanced, very impressive and very sophisticated (based usually on some renaissance white dude writing ridiculous stuff on magical african kingdoms)
- Kongo was an empire
- Zimbabwe was extremely sophisticated
- USA was created mainly by Africans
- etc

What is the sad thing here, I think it is safe to say something exactly opposite - Subsaharan Africa has been always the least developed of all continents in terms of 'civilisation'. Sorry, I did enough research to conclude like that.
Some big but ephemeric empires and vast areas of primitive tribes/slave kingdoms, almost no written languages, no 'high culture' except parts of Western Africa (Islam) and Eastern Africa (Islam, Ethiopian Orthodoxy), most of government systems no more sophisticated than despotic monarchies, and architecture which is less developed than Indigenous American one. With few exceptions (Mali, Ashanti, Ethiopia). Sorry but if Great Zimbabwe, regarded almost as the greatest piece of architecture in Subsaharan Africa, looks like mediocre Polish castle somewhere in the Podlasie...
The ideal is to accept the European dominance, but to remember the other great civilizations for all around the globe.

Generally speaking I am calm about Eurocentrism as long as I don't see the 'Greatest Books in the World History' list on which 90% of works are from Western Europe. Then I enter rage mode.