I think you misread the wiki page there. The Ljubljana Wheel is dated to 5150 BP, (before-present), rather than BC, (before-christ), thus corresponding to about ~3150 BC. This is still really early, but it does place it after the emergence of early urban centers in West Asia, Northeast Africa, and the Indus Valley.

Nationalism heavily influences the popular perception of history in much of the Balkan countries today. Consider the popular Illyrian movement of the early 20th century, in which mostly Croat nationalists claimed to be the descendants of and successors to the ancient Illyrian people, and used this to justify their calls for an "Illyrian State" centered around what is now Croatia, Bosnia, and Herzegovina. A very similar claim of descent from the ancient Thracians was used by Bulgarian nationalists to justify the expulsion of ethnic Greeks from Bulgarian controlled regions of Thrace.

In the case of the Neolithic Balkans and areas surrounding the Danube, various pieces of archaeological evidence have been construed as evidence of a "great civilization", and the Ljubjana Marsh Wheel is just one of many examples. Serbian Nationalists have seized on the Vinča symbols to make the outlandish claim that Serbs invented writing, and that the Serbian nation has existed for over 6000 years.

But whether the Ljubljana Marshes Wheel or the Vinča Symbols represent evidence of a "great civilization" is almost completely subjective, since 'greatness' is not something which can really be measured. Is a civilization any society that farms? In that case, you can argue that peoples along the lower Danube River (modern Bulgaria & Romania), which first started to grow wheat around 5500 BC, represent the first European civilization. But if a civilization is defined more narrowly, requiring the formation of large cities and towns, complex socio-economic hierarchies, and extensive division of labor, then you can argue that Europe's first "great civilization" began in Greece as late as 1600 BC with the emergence of Mycenae.

But wait! We have pottery and religious burial sites in Plovdiv from 4000 BC. Surely that must be the first great civilization!

But wait! What about the Sesklo site? We have evidence of cattle herding in Greece as early as 6300 BC!

But how can you call a bunch of filthy cattle herders "civilized"? Surely, the Golden Hat of Schifferstadt, with one of the oldest calendar systems ever, proves that the first GREAT civilization was along the German Rhine 1400 BC!

But what is more civilized than writing? Surely the first great European civilization then was the Minoans, 1800 BC.

But surely the Vinča symbols are a writing system, proving that the first great civilization must have been in Serbia, 4300 BC!

Ultimately, there really is no way to say what the first "great" civilization in Europe was. Its purely subjective--one man's great civilization is another man's barbarian savages. But while we can never give a satisfying Yes/No answer to that question, there are other questions that can help us to understand the development of Civilization. We found that people living in Slovenia more than 5000 years ago were already using two-wheeled carts, which implies that they must have been carrying large amounts of something (or things) across long distances. What were they transporting? Were they hauling timber to build wooden houses in grassy fields? Transporting copper ore to another village to trade for wool? Could it even have been part of an early chariot?

What we can say for certain is that, in what is now Slovenia around 3000 BC, wheeled carts crawled along unpaved roads. Wheat and peas were grown to make flatbread for people living in wooden houses. Cattle were herded for their milk and meat. The dead were buried in graves, often with additional grave goods. Ceramic pots were used to store grain, water, and various other things.

Our understanding of the Neolithic Europe continues to evolve as new sites are uncovered and new techniques allow us to study aspects of ancient societies that were previously impossible. Without any written records to study or giant monuments yet uncovered, it is doubtful that the early agricultural peoples of the Danube River Valley will attract the same amount of historical interest as the literate ancient societies of Egypt and Sumeria have. But as our body of archaeological evidence grows, so too will our understanding of how ancient humanity lived, and how their lifestyles and decisions would shape and reshape human society over the course of previous millennia.