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I just don't see how to win here without resorting to war. Occupying 40% of the galaxy is only possible by conquering other planets, as there's limited space. Maybe there are some tricks with diplomacy or federation, but for now, the simplest option seems to be gradually enslaving/genociding/subjugating other empires, hoping that the AI federation won't gang up on you. Although, this is exactly the kind of gameplay I was aiming for when creating the race, so there's nothing to complain about.
The developers have repeatedly stated that the victory conditions in Stellaris are placeholders. And you can come up with anything to achieve victory. For example, become a vassal of an awakened empire and help it triumph over its old enemy. And often there are situations where you have effectively already won. For example, if no one can do anything about your federation.