It not sustainable but the other way around.
I recommend to see the lesson "The Greatest Shortcoming of the Human Race Is Man’s Inability To Understand the Exponential Function." from Albert A. Bartlett.
Western countries like the USA may have a dwindling birth rate which compromise the eternal growth myth without immigration. But as a whole the world population is growing exponentially. This isn't sustainable at all. It's a bet when the boat is full (technological inventions may shift this line), but once it's full the decimation begins. There are many possible ways for this but only a very few aren't brutal. One of this few is to have fewer children. But even this can be hard if no social security is available for the elderly. And of course the religious zealots are hard to convince about this.