Is there a consensus on when history began?

The discipline of history begins with the changes in western writing about the past that we associate with Ranke and his contemporaries. These changes broadly moved the proper subject of historical discourse to be the explanation of the past as it was. Prior to the changes associated with Ranke, writers used the past to exemplify moral tales. Additionally as the standards of discourse were moralising, the documentary record of the past was discounted in favour of moralising: people made up edifying stuff before Ranke. After Ranke making stuff up, or even not reading widely enough, could end a career.

The discipline of history, which originated as a “western” writing style considers history to be the analysis of the documentary records of the past (with rules about how analysis is conducted). As the subject of history is the documentary record of the past, history in a “western” sense begins with the beginning of the documentary record of the past: chiefly the written record but also high quality oral transmissions.

Western cultural traditions allow for a plurality of opinions. They also support “authority” particularly in self-reinforcing academic traditions. While some religious or cultural traditions in western culture claim history is other than what historians say it is, historians currently monopolise research funding in widely recognised universities.

For example, some people in western society consider “history” to be whatever the King James Version of the bible says. While Western societies allow these people to hold these beliefs, they’re not imprisoned, the esteemed knowledge systems of Western culture dismiss this belief. “History” as if it were biblical literalism is consigned to under recognised theology faculty in under recognised privately funded religious universities. (The scholarly discipline of theology is considered to be a valid scholarly discipline. It makes text dependent claims on appropriate behaviours and God’s intervention into the world. Scholarly convention generally considers that theological claims about God’s texts regarding past occurrences are a different form of knowledge to “history,” replete with scholar approved caveats and explanations. Correspondingly KJV supremacy has vanishingly little acceptance in this community. One could suggest that theologians are paid to exegete and that literalism “destroys their trade,” in comparing dubiously sourced documents. But the scholarly discipline prefers a more document analysis focused behaviour.)

Returning to history, and pseudo-history, for example, some people in western cultures consider real knowledge about the past as only being capable of being produced by groups of working class people working together. Sometimes this is accepted by western knowledge systems where the work meets the standards of the scholarly discipline, Wendy Lowenstein’s oral histories for example. However, the internally focused rantings of minor Marxist sects who honour the leader’s moral judgements above the documents are rejected by the western scholarly community. History as “praxic co-learning” has been confined to Marxist parties, at the point where this interfaces with scholarly history only those worker’s and people’s histories which conform to scholarly standards have been accepted by the scholarly community. The rest has been confined to propaganda pamphlets and the back pages of orthotrot newspapers.

The most accepted scholarly view is the above. The most accepted view is your local nationalist bastardisation of “1066 and all that”. Aussie Aussie Aussie. Oik oik oik.

History is referred to the first written records know until now, which are the Sumerian cuneiform clay tablets, around 3300 and 3100 BCE.

There are many other ancient writings, but these cuneiform tablets are the oldest ones proven that are coherent, dated (from their authors) and recorded actual events.

It depends on which history you mean.

As an academic discipline, "history" is usually taken to mean the human past, and thus began with humans. This could be the emergence of h*m* sapiens (300,000 BP), or stone-tool wielding h*m*ninds (3.3 million BP), or even further back, the evolutionary divergence of humans from chimpanzees.

Specifically, history in the sense of "recorded history", began by definition with the first written records - this is also the traditional domain of historians, and what hence what history usually means when not otherwise qualified. What occurred before that is held to be "prehistory", for which archaeologists are our main source. Finally, the often chaotic transition from prehistory to (recorded) history can be termed "protohistory".

All three terms describe a part of (human) history, and is often referred to simply as "history" in common parlance (though this is especially so for recorded history). It doesn't help that the lines between the three can be very blurred, as you can see from the Chinese example. Moreover, although writing developed as early as 3,000 B.C., it took thousands of years to spread to all regions. Thus, the delineation between (recorded) history and prehistory differs by location.

Beyond human history, there's a variety of other meanings. For geologists, geological history began when the Earth formed 4.5 billions years ago.. Similarly, to astrophysicists cosmological history dates back to the Big Bang as pnuts mentioned (or possibly even before per @DevSolar).

None of this is particularly "western", though - the Chinese for instance also makes the history/prehistory distinction, although their terms for it are "credible history" and "dubious period" respectively.