It's not forgetting death that's the error; it's forgetting that people have 2^30 ancestors from 30 generations ago rather than just one. Everyone's family tree grows exponentially, but they all overlap.
There had been roughly 120 billion humanoids living (and dying) so far. Not sure where cut-off line between apes and homo sapiens exactly is though. The growth is +- exponential. So 1 billion doesn't mean much (and yes all overlaps with other trees, so voila we have present). Plus many people died before having kids, tough times it were.