Rrerku

The WH40k wiki states that Khorne, Nurgle, and Tzeentch all came to being during Earth's middle ages - at most only a few hundred years apart from each other. The descriptions imply that it was Earth's events who marked their birth.

[Khorne] is the mightiest and the oldest of the four major Chaos Gods, fully

coming into existence in the Immaterium sometime during Terra's European
Middle Ages in the early 2nd Millennium, his birth heralded by an era of
wars and conflict that raged across the globe

[Tzeentch] was the second of the Chaos Gods to come to full sentience within
the Warp, sometime during Old Earth's Western medieval period in the 2nd
Millennium. His birth marked the maturation of human nations and politics

[Nurgle] is the third of the Chaos Gods to fully awake within the Warp,
emerging during the 2nd Millennium in the midst of Terra's European Middle
Ages, as great plagues swept across the world heralding his birth.

At this point in the history of WH40k, there have been multiple galaxy spanning wars that have ended entire races of godlike beings. But a few dozen million warring, diseased, plotting Europeans millions of years later were the creation of the entire Chaos pantheon at this point in the WH40K universe?

How weren't they born earlier?

You are mistaking cause and effect: Chaos gods haven't been born because there was war/plague/political manipulation happening on Earth, but the events on Earth have happened because the gods were born.

In the first and second millennium, humanity's impact on the galaxy was next to non-existing¹: yes, the Emperor was already alive, but he was pretending to be barely a local leader. At the same time, Eldars and Orks were alive and thriving for about 60 million years, together with many more (currently extinct) races and civilisations.

Lets take for example Khorne: yes, there was quite a bit of fighting in the middle ages, but there were wars claiming many more deaths before that (The Crusades claimed "barely" about ~1.7 million deaths, which is comparable to the Punic wars (264 BCE - 146 BCE) and much less than for example the Three Kingdom War in ancient China (184-280 CE), which claimed over 37 million deaths (source).

As for the question "why the gods haven't appeared earlier" - we can only speculate. Most likely there were no civilisations powerful enough to create them - whenever a race had a strong presence in the Warp, it would attract the Enslavers - a race of psychic parasites - which were able to wipe whole planets.

Please remember, that Eldars created barely one Chaos god and were almost destroyed as a race - imagine what would happen if humanity created three of them...

^{1 Although, apparently some times during the early Medieval period the Emperor (as Saint George) has imprisoned SOMETHING under the surface of Mars. That "Something" is most likely C'tan known as Void Dragon, this is not exactly confirmed (or denied) by the GW}

EDIT: This information apparently also has been retconned sometime in the past - currently it is assumed that all gods except for Slaanesh were born after the War in Heaven, ~60 million years ago.