Primordial human in one of the nights, trylying in a cave trying to sleep, his ear on the ground while laying in cave.

Chickens lay eggs; people lie down.
"Trying to sleep" would be the correct phrasing of your original sentence, but the order I've suggested feels more natural to me.

But at the moment one get the silence,silence falls, he begins to hear a sound between his ear and the stone he is laying on .

He becomes afraid and move aways his ear away with a sudden rush, and the sound vanishes.

Later when he layies down on, his side to the ground, he begins to notice the sound again.

A short speatking with the same intervals.

Not sure if you intend "speaking" or "beating" here; either would work.

This human hears his own hearthbeat.

"This human" feels a bit forced (though not wrong), but it could be a stylistic choice.

And he starts mimicking start, which is the biggest proof of humans are comingcame from monkeys.

Human comes to the conclusion this sound is stemming from two object is hitting each other whereas. So the human gets a stone and hit it to ground with the aim ofstrikes the ground, trying to repeating the sound in his ear , he hhe heard in his eard.

For a while he does it accordingsteadily.

Not sure your intention with "accordingly," which doesn't fit here. I would suggest something like "steadily" if you are attempting to say that he beats the stone in time with the rhythm of his heartbeat.

The only musical element in here is repetition.

Later, this sound evolved into new slower or faster rhythyms.

And humankind comes to modern drums from this repetiton of hitting sounds. Even create nowadaysing modern drum'n'bass style.

When iI was interested şin music i was, I read important archives in my brain.

Not sure what you mean by "I was archives"

But it's over.

Now I only listen to my heartbeat.

My favourite and only listenedmusic is the group of ' 'The Veins'.' Excellent Oorchestra.

They are playing non-stop. Uncapricious.