I recommend Return of Civilization to you! The protagonist of this book woke up from the hibernation chamber and found that the Earth had become a desolate ruin. Finally, he brought a disintegrated warship and a smart AI in the shape of a girl to find a new civilization. Although the main character didn't directly take the surviving humans, it was still a story about a warship searching for a new civilization after the end of the world. I hope you like this recommendation. Muah ~