You are quite right that capitalism is predicated on growth. Think about that for a moment.
What do you think happens when growth is no longer there? What do you think happens to capitalism?
As for Malthus, his arguments rest on one premise, that food production is an independent variable from the size of the population. But we know that this is not so. Like anything, the laws of supply and demand dictate that when demand rises, so does supply. When demand falls, so does supply in response.
Ergo, as most foodstuffs are inelastic goods, the production of food is a dependent and not an independent variable. We would expect greater land cultivation in response to greater demand. Which is what we do see. We would expect as the price of food goes up, that new technologies become viable in the production of food. Things like mechanical harvesting. Reducing the labor costs makes food that much more cheaper and increases yield.
If someone asked a man in the middle ages, how high that a man could climb, do you think any would believe it to be possible for a man to climb to the other side of the moon?
The only limitation on food production is really the cost of energy. With sufficient energy and low enough costs, you can grow sufficient food to feed the population.
So you think 7 trillion people can live on the earth, along with trees and birds and all that good stuff, no problem?