I would guess that's unknowable. The old proximate vs distal cause problem is hard enough for simple cases, let alone something like the interactions between thousands of ecosystems, 7 billion chunks of primate psychology, and global civilisation. I am sure that capitalism is incompatible with the continuing existence of healthy living ecosystems. So (for me) your question comes down to: is capitalism inevitable (& even if it wasn't, are we now stuck with it for historical reasons?).
We can look at some things that seem salient. When you look at human societies over time and space, the vast differences in cultures are astonishing. Most people have little idea of just how different cultures have been, so their concept of 'human nature' actually just labels their own culture (I'm not suggesting that's how you're using 'human nature'). Even the subset of contemporary 'capitalist' nations are greatly variable, not the least in their levels of ecosystem destruction.
Then capitalism itself, variation notwithstanding, does depend on the metaphor of growth (I insist on 'metaphor' because nothing defensibly 'grows' in the process of deconstructing complex evolved circular systems to build simple technological ones requiring ongoing inputs). Some think this can be fixed by building 'circular economies', but I've seen nothing to suggest that this is possible at all, let alone on a relevant timescale.
We know for certain that the 'growth' metaphor/ideology doesn't spring cleanly/directly from human nature, as there's no shortage of human societies that have lived in a relatively steady relationship with their environment (here in Australia for 60,000 years or more).
So who knows? Perhaps H. Sapiens can get free of the system it has made, perhaps not. If it can, it's not going to be in a hurry, so we'd need to slow down the rate of destruction while still capitalists. I do think that's possible with appropriate application of tech, "electrify everything", tough corporate regulation, land set-asides, urban greening, etc. But because of compounding, even slow dismantling of ecosystems eventually destroys them. So H Sapiens still needs to ditch capitalism at some point.
There's certainly no guarantee that it can, because evolution, in making the species, wasn't looking to the future (and certainly not to a destiny).