Just note that there are two options to join Survival. One will start the game in 6 minutes (I am ~95% sure of that time) regardless of whether there are any other players in the game. The other one, which I think is the matchmake option will take much longer.
Honestly, the solo runs where I never find sign there is other players are my absolute favorite. I don't have to struggle to find resources, but it also makes it more intense because no Calvary will come and help if I go down.