There are myriad of examples of Humans wreaking havoc on ecosystems prior to the industrial revolution and I'll try to provide you with some examples and a brief explanation of why they collapsed here.

Easter Island: Easter Island is probably the most obvious of all ancient civlizations to cause their own destruction as evidenced by the enormous Moai (easter Island heads) that dominate the island. The commonly held hypothesis for the fall of the islands civilization is that the population became fixated on creating the Moai which served as symbols of welath and status to the various families and tribes. The island was once heavily forrested but over the course of centuries the forests were destroyed which devasted the ecosystem. One the forests were gone it was impossible for the population to continue creating the Moai but it also undermined their ability to support their complex society which they had developed.

Pitcairn Island: Pitcairn Island is located in the southwest and was once home to a complex society based on trading with nearby island societies. In this particular case the population harvested resources from the shores of their island and traded it with the populations of the nearby islands. Though I cannot remember exactly how the trading relationship worked essentially once island had good raw materials for making tools and the other had good offshore resources in its shores. Unfortunately over fishing and harvesting devastated the wildlife and lead to a collapse in the trading economy which eventually led to the extinction of both islands' societies.

The Maya: The Mayans, as we all know, had a thriving civilization in Central America which essentially vanished overnight. The hypotheses I subscribe to is that through deforestation they decreased the amount of rainfall they received which caused their water sources to dry up. This led to increased competition for water which led to greater infighting and eventually the death of the civilization.

The Greenland Norse: Though the Greenland Norse may not have directly influenced their own environment to their demise to the same degree as the previous examples they certainly did not help themselves much. Having arrived in Greenland during a relatively warm period they were able to colonize the island with relative ease but when temperatures started to cool again things became more difficult. It was also during this time that inuit populations first began arriving in the area and the two societies began to compete for resources. The Norse also cut down most f the native forests which decreased the resources available to them and refused to take lessons from the inuit who managed to survive well past the decline of the Norse population.

This is mostly based on Jared Diamond's Collapse which is about this very subject (and I literally just packed it up because I'm moving shortly). I highly recommend it as he is able to do much more than I was here and provides many more examples as well as explanations for the systems which led to these events.

There is quite a bit of evidence that Native American populations altered the landscape by "clearing and burning forests" (source). That same source indicates that there was a noticeable change in carbon emissions as far back as 100 B.C. because of these behaviors.

Another study showed that oak, hickory, and chestnut groves are highly correlated with native habitation in NW PA (USA). (PDF source) They do indicate that the cause/effect is not well known, so native populations may have lived in these forests, not created them. However, they also discuss how some known practices of native populations could lead to these groves increasing in size because of their habits.

While these aren't extinction events, changing of forests can lead to changes in animal and plant populations, so I figured that would be relevant to the topic.

I have heard, mostly third-hand, that human changes help push areas in the middle east from grassy plains to desert as we see now. I could not find anything scholarly on that topic, but someone more well versed may be able to correct me on that. Removed because it doesn't seem as relevant to the question as I thought when I typed it.

You can also ask this in r/biology, I am sure they can give you a lot of answers.