In the early Eocene, 50 million years ago, the sea level was hundreds of feet higher than today. There were no great ice sheets. The climate was extremely hot, despite the Sun being about half a percent weaker than today. The high temperatures, almost certainly due to active carbon from massive volcanism (which would also have reduced the volumes of the ocean basins) are clearly shown for instance by fossils from the bed of the Arctic Ocean. It's no accident that the hippo-like ancestors of today's whales took to the sea at that time and became fully aquatic within a few million years.
Today's buildup of active carbon from fossil-fuel burning has irreversibly changed the state of the Earth system. See the books by Archer and Lovell and their lists of further reading. Therefore it's possible that the nearest `dynamical attractor basin' is already Eocene-like, though it might take many centuries to reach it. So if human civilization survives -- and that will be a close-run thing as the sea rises -- there might still be time to develop industrial-scale carbon capture.
There is a simple reason why current climate models cannot tell whether the Earth system is, or is not, already being attracted to an Eocene-like state. The models are not good enough to make sufficiently accurate predictions of (a) snow accumulation rates on the great ice sheets, and (b) ice-sheet depletion rates by heterogeneous ice flow. Whether or not we are heading to a new Eocene depends on the difference between (a) and (b). The models cannot credibly predict the sign of the difference. Still less could they guide us through the risks of `geoengineering'.
We might get lucky. The Earth system might still be stable. Today's Earth has a beautiful fluid-dynamical climate regulator, the Antarctic Circumpolar Current, that was absent during the Eocene. That might be enough to compensate for today's stronger Sun plus this century's accumulation of active carbon. There might still be time to undertake the only safe, or relatively safe, form of geoengineering, `air capture', meaning carbon capture from thin air. That has already shown to be feasible and affordable -- about as affordable, perhaps, as was the Great Wall of China, that is, affordable as soon as the political will is found, which might become possible once the sea has risen some fraction of a metre.
Whether there is enough time left, no-one knows. This is not alarmism. It's just recognition of the current state of knowledge.