Birth control.
If the population grows freely it will always expand to the point that just about everyone is in poverty. That's why it's our natural state. The only way to avoid it is to keep our population well below that point.
If the problem were simply too many people, there would have been a Golden Age in the past when there were just the right number of people. But there wasn't.
Oh, and your hypothesis flies in the face of natural history. Populations of mammals don't grow until "just about everyone" is starving (animal poverty), they grow until a handful at the fringe are starving - but not for long, because the predators eat them.
ETA: there is more than enough food to feed everyone. there are more than enough resources to house and clothe everyone. Americans throw away enough food every day to feed 40,000 people for a month. Resources are being thrown into landfills in the "have" nations, instead of redistributed. But the concept of redistribution of wealth scares the crap out of those who wish to profit at the expense of others.
It's the resources per capita that counts. There used to be fewer people--but even fewer resources.