Your worldview is likely very wrong. The population growth is not a "sustained" state - it's an artifact of the transition from poverty to prosperity. Once a country has low child mortality rate and high education, the birthrate drops like a rock - you know, even China, which isn't that rich overall yet, has its birth rate drop below that of US - i.e. China's population growth has already effectively stopped (the actual number of people will continue to grow as the current population grows older, but the number of children won't change much).
You may want to watch:
https://www.gapminder.org/videos/population-growth-explained...
and a few other videos on gapminder.
> we only have a fixed land/resources in our planet and we must stay within carrying capacity.
There's no evidence that's the case. We do have serious environmental issues (like global warming, and pollution) but they are not directly related to "carrying capacity" to sustain the overall human population. For all we know, we know we can produce enough food to sustain the population. We know technological solutions to solve the global warming.
Look at the historical data on birthrate (click play to see it change from 1800 to present):
https://www.gapminder.org/tools/#$state$time$value=2018;&mar...
you'll find that the world has largely already converged to the steady state, and it's only Africa that needs to finish its transition to the sustainable state. Thus, the only humanitarian and practical way to end the population growth is to get the (most African) poor countries get better health, better education and economy, which is already in well progress.
