If it is fake, I'm going to lose my flair!

Short answer: It was real. I suspect what has happened is that people have confused that there is novelised, heavily fictional version of the war (that was created a long time later) and the era, they know it is fake and forget there was a real war and real era.

We have writings from contemporaries and the records were created by people of the time as part of Wei and Wu's history projects and Shu's record department then compiled by Chen Shou an officer of Shu (one of the kingdoms) and Jin (the winners). Later historians and commentators wrote about it which was then added to the texts as annotations by Pei Songzhi (including from scholars like Wang Can, an officer of Cao Cao as well as Liu Biao). We have poems (including from Cao Cao), we have tombs, we have major changes including Sun's transformation of the south or the theological and philosophical changes. For it to be fake would require explaining away what happened because of the Han's collapse and Jin's rise (including how did they become unifiers of China and a recognized dynasty if the war didn't happen) and all that came about because of that war.

What I suspect people are thinking of and may have got misunderstood over time is the era has been greatly mythologised rather than the era never happened. After the civil war would be... well more civil wars and invasions from abroad so people looked back towards the Han as a golden age. Storytellers, playwrights and the likes would tell of Liu Bei, the sandal weaver turned Han Emperor, and his brothers (sometimes with Zhuge Liang as the sage adviser) fighting against the mighty, crafty northern power Cao Cao. Guan Yu became part of a religious contest for followers and a subject of popular plays with things like Guan Yu's 10,000 li journey or fictional son Guan Suo.

Then, over a thousand years later, we get the novel Romance of the Three Kingdoms by Luo Guanzhong, considered one of the great classics of Chinese literature. It took popular tales and combined them into one big narrative covering the whole of the era and has had a huge influence on how people see the era and its characters. It is, of course, a work of fiction but people can underestimate how much of it is fiction. That three kingdoms isn't real, it's the way of fighting, dynamics and characterization is fiction using a history platform and bears very limited relation to the historical three kingdoms. However the era itself was real, just like movies and TV shows about Rome or WW2 may be heavily inaccurate but Rome itself existed and WW2 did happen.

In terms of Cao Cao never existing, the novel does include fictional characters from other works (Guan Suo, Zhou Cang) or create many of it's own for kill fodder, plot points and the like. Was Cao Cao one of them?

I haven't seen those arguments and I wonder if it might be the way he gets seen might seem exaggerated (as well as the era is fake claims). People remember his brilliance as a warlord, his major victories (and some of his defeats), his dominance in politics, sometimes his administrative reforms, arguments about his brutality. He can be portrayed as a calm, brilliant figure and perhaps that has made him seem mythical but his many mishaps or his very emotional side that show him as more human can get forgotten.

But yes unless everyone involved in the era was engaged in a massive prank, faking records, someone in the rival state of Wu making an attack biography in the Cao Man Zhuan and Chen Lin writing a call to arms against Cao Cao for giggles, he was real. If he did not exist, where did Wei come from, who unified the Central Plains, why did Jin claim the Mandate from Heaven from the Wei dynasty created by the son Cao Pi?

I do hope this helped and please feel free to follow up with any questions you might have.

Sources:

The SGZ by Chen Shou, annotations gathered by Pei Songzhi translated by Yang Zhengyuan. Including the Annals of Wei with Cao Cao's biography.

Rafe De Crespigny, one of the leading western experts on the fall of the Han and the civil war pre 220, Imperial Warlord: A Biography of Cao Cao 155-200 AD