I don't think there is any natural system or process that grows indefinitely without reaching some point of saturation or satiation. It's kind of hard to imagine what eternal exponential growth even looks like.
Also, it probably is not possible for the richest countries in the world (that also tend to have the largest ecological footprint) to continue growing sustainably, since we are already emitting (for instance) way too many greenhouse gasses, and need to radically reduce our output of them, not just slow its growth, or even flatten it.
But eternal growth as a human goal really doesn't make sense. How many toys can you play with? How much food and drink can you consume? At some point, a sane person is rich enough, and doesn't need to get richer.
But capitalism depends on growth. My possessions may give me pleasure, and content me, but they are literally valueless to the capitalist. The capitalist, qua capitalist, is only interested in what he can next sell me. Of course, things need to be replaced, from time to time, but capitalists have never seemed satisfied with a replacement-value economy. Capitalism cannot survive stasis.
Of course, the immediate problem is that wealth is very unevenly distributed. Many people do NOT have enough possessions, let alone enough security in them, to be happy. Redistribution is necessary. We've been told, in the past, that growth will raise all boats so that the poor will eventually be comfortable and secure. It doesn't work. The Kuznet curve has been debunked. Redistribution is necessary. Growth (if it doesn't destroy the habitability of our planet) may make it a little less painful to redistribute (maybe we could approximate some Pareto optimality or a Rawlsian "give to the rich only when it benefits the poor"), but redistribution is still necessary.
Personally, I believe the planet is rich enough, or close to being rich enough, if we distributed it's fruits more fairly. I don't think any further growth is really necessary, but certainly it needn't (and can't) go on forever.