I can't answer that JC, but I think we will find alternatives when it's not cost effective to extract finite resources. There will be a stall in growth while we do but I think generally we can go on . I still the the key problem is over population. Even. If we stopped population growth now I'd like to think we are capable of using what we have in better and better ways. Maybe not endlessly, which I suppose is your key point .
There are many ways to achieve infinite growth that don't involve consumption of additional finite resources. In the post-industrialisation West much growth seems to come from extending production cycles to include additional steps.
At its simplest the production cycle for food is person A grows food then person B buys food directly and eats it. We now have food production cycles that include building and maintaining machinery, producing pesticides and fertilisers, transportation to factories, transportation from factories to distribution centres, transportation from distribution centres to shops, staff at each of those steps, management/HR, IT support, advertisers, researchers, analysts, website developers etc. I'm sure I've missed some and I'm also sure people will find new ways to include themselves in that cycle in the future.
It only feels like a few years ago that ordering a takeaway meant going to the takeaway or ringing the takeaway. Who knew we needed to spend £1.5bn a year for Just Eat - amongst many others - to position themselves as middle people in that process? GDP growth - yay!
When I went to India there was a person whose job was to take the ticket from a car leaving a multi-storey car park and put it in the machine. The machine being about one foot away from the window of the car. I'm sure we can dream up plenty more jobs like that. Dig a hole and refill it, endlessly.