We did discover they are not invulnerable. The destroyers that darkened our skies like a plague can be harmed.
I believe this states here that the fleet that was used to kill the Ancients was much, much more vast. Shivans bombarded Vasuda, but in the cutscene showing the destruction, there is no massive fleet "darkening" the skies. I believe the Shivans likely had to dispatch a much larger fleet to kill a much larger enemy, causing this. Also, as stated above, if fighters never were killed, the numbers would become severely one sided very quickly.
If there was a massive fleet attacking the Ancients, then the "no shields in subspace" information would do them little good and wouldn't have valued it as they did, trying to pass it on to future civilizations. Sure, they knew how to destroy the Lucifer(s), but what about the rest of the fleet? However, if you can't even kill the fighters, then find a way to kill them, that is information that you would hold dear and try to preserve, even if you die.
If the Ancients would not be able to kill even fighters, this war could never take very long... and you forget, that all ships bigger than fighters/bombers do not have any shields. So they were at least able to destroy transports.
I do believe that the war was over pretty quickly, only lasting longer than the Great War because of the size of the Ancients' empire. And I did not forget that non-fighters/bombers don't have shields:
Sure you could destroy the unshielded capital ships, but not when you have fighters you cant kill firing up your butt all the time.
All in all, it seems like the main reason why the Ancients were defeated was they learned too late how to bypass SOME type of shield. If it was only the Lucifer(s) shields, then the Ancients would have defeated the rest of the fleet and you would have only the Lucifer(s) going from system to system. Even though the Shivans could have destroyed all the Ancients' worlds, you probably could outrun a few destroyers and hide somewhere. If it was all shields, then you still have a full fleet that you can't outrun for long.