re: The climate is *always* changing.
The vast majority of invasive species are ignored - only the worst of the worst get any attention, usually not enough, and usually long after they should have.
Not a good example for your point.
And here in the SF Bay Area, you can go into the little remaining old-growth redwood forest and find not only the particular piece of ground would look much the same a thousand years ago, but that many of the same individual trees would be there.
Aside from places near ecosystem boundaries, you need more than a thousand years before you'd see "amazing" changes.