It's a story as old as humanity. There's many examples of humans exhausting their nearby resources because they thought they were effectively infinite. Whether that's a forest, a food stock, a water source, or something else.
And every time it's happened in the past, the solution has been to leave. There's always been somewhere else to go.
Not every time, or at least the solution doesn't always result in everyone surviving. The Mayan civilization, for instance, is thought to have exhausted their local resources and fallen apart as a result.