From at least one resource's interpretation of Cosmism, it sounds like that just might be what you are looking for:
Cosmism is an existential philosophical orientation that sees the survival of mankind and of the individual as part of humanity's "common task". The migration of humans into space is seen as inevitable, since it is essential for humanity's long-term survival.
-- What is Cosmism?
So, that is your answer from a philosophical perspective. There could be one or more new religious movements that espouse these views, but I haven't found any in a cursory search.
It is also interesting to note that survivalism in general anticipates a coming disaster that will affect humanity, and survivalists usually try to ready themselves to survive whatever event(s) may come. In this sense, cosmism could be seen as a variation of survivalism. To some extent, anarcho-primitivism could be seen as being at the opposing end of a spectrum of survivalist views, where anarcho-primitivism says we need to return to a more primitive* state to survive and cosmism says we need to advance.
* "Primitive" here is not meant as a value judgment, just in the literal sense of a more original state.