Like all models, incorrect but useful, I think that the most useful model to view "value" and GDP is as a crude approximation of the human input that goes into making something or making it useful. Natural resources are only useful if humans exert effort to extract and refine them, services are only useful if some humans exert effort to save other humans more effort, manufacturing is only useful if the effort exerted is repaid in improved productivity or utility gained, etc. Once you abstract away from monetary units to say that we're all trading units of human effort at varying degrees of efficiency, it's clear that GDP growth and "the ability of limited resources to support a growing population" is dependent on the growth of both the amount and the efficiency of human capital rather than physical resources. I'd take Ehrlich's wager [0] at any point in the future.
[0] https://en.wikipedia.org/wiki/Simon%E2%80%93Ehrlich_wager
The Earth has finite resources, and is replenishing them more slowly than we're using them. You're making the argument that withdrawing exponentially increasing amounts from our sizable savings account is just fine, thank you on the assumption that it will never run out.
This is a clear failure in understanding of the exponential function.