The question of 'finite resources' comes up a lot when it comes to growth, and the question essentially betrays a lack of understanding of what growth is.
We can definitely grow by 3% per year forever, it's easy if you first consider we don't need any real material change for that to happen - it could just mean the 'numbers on our money change' i.e. just inflation.
But more likely, there will be material progress and 'growth' for the next 2000 years, just as there was for the last 2000 years. (Mind you, most of it has been since the dawn of the industrial revolution).
If you open your mind just a shade and consider how vastly the world has changed over the last 100 years alone, it's not hard to imagine how things could change in the next 100. I was alive when the internet went from nothing to 'world changing' and nobody - I mean nobody really guessed at the profound changes it would mean. There were a few thinkers who got a few things right, but nobody had the faintest idea. The same can be said for the dawn of the automobile/airplane one century ago.
There are a few technologies on the horizon which could shatter our world view, namely quantum computing and fusion. Just to name two that we know of.
We don't know if they will fly, but if they do, it will change everything.
Quantum computing may imply de-facto near unlimited computing for everyone. Consider that Deep Learning was only on the chalkboard until we had cloud computing, imagine what we will be able to do when it takes 0.1 seconds for insanely complicated neural networks to 'learn'?
If fission flies, it could mean unlimited energy for everyone. Imagine if the cost of electricity went to 0.0001 cents/kwh? What does that mean? It sounds crazy, but remember that 200 years ago, before the dawn of the industrial revolution, you did it 'by hand, or by horse' hence 'horsepower' as a unit of measure. When coal and machines came around it would be comparable to fission happening now - the world literally came out of the dark.
Vast changes are afoot, and will be for a very long time as long as we wipe ourselves out by some series of stupid acts.