FWIW, this view is normally referred to as [cornucopianism](https://en.wikipedia.org/wiki/Cornucopian): this debate has been raging since at least the 1960s, and there are some interesting links from the Wikipedia page.
Therefore we know there is some limit - and we are just arguing about where that limit is.
The Global Footprint Network with their "Overshoot Day" believe we are already beyond that sustainable limit and, to be honest, with increasing populations that (quite rightly) demand Western living standards, I doubt we will ever be sustainable.
If we're allowed colonization of space, we can only travel at a finite speed. Humans can overtake a finite radius in a year, resulting in a cubic rate of growth in volume. Exponential growth is ultimately limited by the finite speed of light and dimensionality of our universe.