I vaguely remember someone telling me about this book. Unfortunately I can't remember who it was and I only remember vague details. The basic premise is that in a post apocalyptic or near apocalyptic future, someone (I think it was a woman) realizes that appeals to people's reason aren't enough to get people to work together to get off the planet, so the person starts creating a cult/religion/philosophy that encourages a focus on space colonization to ensure humanity's survival. That's about all I can remember.
This question is sufficiently vague that I expect multiple books could fit it. One of them is "Parable of the Sower" by Octavia E. Butler.
The book is told from the viewpoint of Lauren Olamina, a teenage girl who happens to be an empath. She lives in a small enclave, in the near future, but society is breaking down around her. Eventually violence comes to her neighborhood and she is forced to flee.
Although the world around is falling apart she maintains hope in an apocalyptic world. She is inspired by a new faith/religion/philosophy that she has invented and which she spreads. It is called Earthseed. Each chapter of the book starts with a quote from 'Earthseed: the Books of the Living' that Lauren writes or inspires.
One aspect of Earthseed is
The Destiny of Earthseed is to take root among the stars
So we have a near, but post-apocalyptic future, a female narrator, and a faith that preaches that humanity should focus on leaving the earth. So it fits the question. But I expect there could be other books that are equally good fits.