The reason why everyone points to Western Rome as an example of fleeting success (forgetting that its eastern part survived for an additional millennium), is that it was the last empire to go out with a real boom. As a counter-example, you could point to the British empire, whose heritage is still alive and well: We are discussing using its language and it is still a part of the G7. The same goes for the Roman language, which is still one of the world's most spoken, just under another name (Spanish). And you probably have dinosaur descendants living in your city, in the form of birds. Things survive, and so will we.
Worrying about imminent ecological collapse is as old as the industrial revolution. Thomas Malthus postulated that agricultural yields would not be able to keep up with population growth. But here we are, more than two hundred years later, better equipped than ever to tackle the challenges ahead of us. I am certain that we will make it out alive, as long as we keep up our good work.