The problem isn't the population today, and that hasn't been my question. That can even be worked out mathematically by going backwards. That's where the assumption that population doubles every 150 years comes from. It does not take into account die-offs, plagues, wars, boons, etc. It assumes, simply, an upwards curve in the population over time.
A small town population of 3000 people, Fisherman? Including young, old, sick, weak, and dead?
The problem is that you're looking at world history through a fun house mirror, and ignoring all the signs of civilization around the world. The very fact that you had multiple empires at this time contradicts your calculated population. The presence of culture in far more distant areas, like China and the Americas, further contradicts it.
The alternative explanation is that there was already a huge population on earth, with patches of advancing culture and evidence left over for anthropologists and archeologists today.