The question seems to assume that “spiritual nourishment” is a need that everyone needs to fulfill. Not so. Many people — atheists among them — will argue that they can do without spiritual nourishment, thank you very much.
To me, spirituality simply means the pursuit of meaning. And the pursuit of meaning can be easily undertaken without belief in the existence of supernatural beings and phenomena.
Human beings are pattern-seeking animals. We find the strangest meanings in the strangest of places. Our imagination has given rise to the most bewildering mythologies and deities as well as the most insightful and profound philosophy.
This body of work is accessible to us all through the internet, books, and recordings. There is plenty of meaning there for anyone who wants to go look. So why would anyone even need to wonder where “spiritual nourishment” is going to come from?
If not from religious traditions, people can always find their own path to meaning in life. There is no reason to think that there is anything resembling ultimate purpose in the universe. Whatever meaning exists, has been collectively decided upon by people. In such a scenario, individuals can always decide what gives their life meaning.