As society decays into a mass of people doing immoral things due to the lack of divine guidance all things will become legal.
As single folks are not going to be able to trump the immoral behavior of other single people, we should form bands in order so that we are the mightiest group.
Now, it stands to reason that there will be other large bands of people and going to war with them would be costly for ourselves and themselves so we should best avoid each other. As hostile actions from my group will cause the other group to respond in kind, hostile actions must be kept to a minimum.
Further, as I don't want to be killed and other people won't want to be killed we should probably avoid the murdering of people. This will also allow for the threat of murder to be more successful. Pirates, for example, would let you go if you surrendered so this sort of kindness without laws has historical parallels.
There's little point in stealing a lot of stuff if I cannot be secure in keeping it. Why steal something that somebody else is going to steal again. At the very least within the group stealing and murder must be abolished. Further, other groups are not to be attacked and merging with other groups or treaties with other groups should be established and maintained.
Without God we'll descend into chaos... and necessarily form the exact same structures we formed before.