at conception, natural man, lost people, as made sinners, are made in a spiritually separated state, just as if they had sinned. This state is not because they had sinned, but because of the consequence of Adam's sin, Romans 5:19.
Adam did not die spiritually because He was cast out of the garden, that physical action simply illustrates the spiritual separation caused by Adam's sin. Isaiah 59:2 Adam and Eve were both spiritually "together with God" until "their eyes were opened." Genesis 3:5-7 Adam and Eve were both created in a spiritually alive state, and they both, uniquely, spiritually died after being spiritually alive.
And yes, we agree, once a person is transferred spiritually into Christ and undergoes the washing of regeneration, the result is they are made spiritually alive together with Christ. The consequence of their sin is removed, the washing, so there is no cause for spiritual separation, and therefore they are "made alive (spiritually regenerated) together with Christ."