About how many years of human existence passed before the world population reached 1 billion?

Bearing in mind that the first billion people was attained approximately by the 19th century (mid 1800 AC) and that the first "Homo Sapiens" is dated back some 200.000 years ago in the southern tip of Africa, we could establish that "Homo Sapiens" is about 199.800 years old. However, recently, and in the the paleontological excavations in Atapuerca (Spain) there have been discovered some vestiges and tools of the so called "Homo Antecessor", which date back to one million years.

So that should be the approximate answer to your question if we consider the "Homo Antecessor" as our most remote ancestor.

It took all of human existence up to 1804 before the world population reached its first billion. Before then, hunting and gathering societies never managed to pass a few million, with scarce food supplies and a nomadic lifestyle limiting growth. The agricultural revolution and the domestication of animals provided a stable food source necessary for population to start growing. Better nutrition and healthcare following the Industrial Revolution accelerated this growth to what it is now.