I'm amazed at this coincidence, too.
Halley's Comet takes 75 years to make an orbit. It goes out to about 35AU. Let's call that 1 year per AU. That rough, rough number would lead one to conclude that anything from the Oort Cloud moving at a similar speed could take, say, 100,000 years to get here even if it was aimed at us. If triggered by something 70,000 years ago, we'd still have a bunch of millenia to prepare.
Anyway. I'm sure I'm completely wrong.
https://phys.org/news/2016-12-ice-ages-linked-earth-orbitbut...