A solution would be to sensitize those countries with the highest birth rates, through the UN. If those countries don't prosper and control their demographics, the situation will remain unchanged.
The problem is not births, it's the birth rate and the growth rate of a population. The population of Europe, America and Australia is not growing that fast. Just think that Europe, which has always been the most populated continent in the world since ancient times, had a population of 414 million in 1940. Now it's 740 million (considering also the massive immigration from the South of the world). In the US,which was pretty empty in the Middle Ages, had a population of 132 million in 1940, now it's 304 million.
So, if we became 7 billion that fast, it didn't depend on Westerners, whose population growth rates are sustainable.
Also the rare presence of big families in America and in Europe counterbalance childless families, which are becoming the majority in countries like Greece, Switzerland, Russia, Italy.
I will have to say it's also something ethnographic. There are ethnic groups which are much more prolific than others.
I would disagree majorly with it being ethnographic. It is a class epidemic. The poor classes of the world have the over population problems even in the richest countries and its easy to see why.
If you don't have a job that gives you 8 more hours to think of sex and possibly have it.
If you don't have money to go shopping, the movies or just out that gives you more time to think of sex or have it.
If you don't have money to buy birth control medicine
If you don't have money you can't afford education
In some countries having more kids can give you more workers
In some countries having more kids is a financial boost to the very poor.
It doesn't matter the ethnicity of these people it is all about the finances.