The answer is less fuzzy than you might think though still rather fuzzy. The key is writing. The past that is written down is history. The past that is dug up is archaeology. This means that the date of prehistory changes depending on where you're looking at and on if you're using it to mean before writing or before record keeping. Writing was adopted at very different times around the world and some uncontacted tribes could still be considered prehistorical.

On a global scale prehistory means before about 3400 BCE when the first writing systems emerged in Mesopotamia and the first records started being kept. However this was only the emergence of the first complete writing systems capable of representing all of a language. Systems known as proto-writing that could only represent numbers and limited concepts, often in a pictorial manner, emerged about 7000 BCE in both China and Europe.

Here's an incomplete list of the origins of independent writing systems (i.e. systems not based on others):

As mentioned previously in Sumer in Mesopotamia pictographic writing was developed about 3400BCE.

Egyptian Hieroglyphics were developed about 3200BCE.

The proto-Canaanite alphabet was developed in Canaan between 1850 and 1550 BCE. This script would go on to become the basis for Greek, then Latin and then English.

The Chinese pictographic language was developed about 1500BCE.

The Olemic language was developed in Mesoamerica around 1000BCE.

Prehistory is also usually taken to mean after about 3 million years ago when the first hominids started to appear and stone tools were developed but technically could go all the way back to the big bang.