What kind of manned missions do you have in mind?
Whatever doomsday scenario you are concerned about, it's not a realistic goal.
But there aren't any spare rockets lying around like that. And we're talking about a standard LEO mission, not a doomsday scenario one off special mission.
Do you know why they beat you into space? It certainly wasn't because they had a head start.
Your universe sounds fun. Can I join?