I only read p.1, but yes- from 500,000 BC to around 10,000 BC, there was no significant increase in population after it stabilized around 1 million people.
People were hunter gatherers all that time. It was a difficult life and lifespans were short. Very few adult pairs had more than 2 children who also survived to adulthood.
Even after agriculture started and growth picked up, there were terrible plagues and wars and still many babies/children died.
The explosion of population is really a problem that started in the 20th century. Very easy to research on the Internet.