It was a garden (park) that God planted for Adam to live in (Genesis 2:8,15). It wasn't where God lived. God would occasionally visit and walk with Adam and Eve, so only then were they in His presence. God drove them out of the garden because:
Genesis 3 (WEB):
(22) Yahweh God said, “Behold, the man has become like one of us, knowing good and evil. Now, lest he reach out his hand, and also take of the tree of life, and eat, and live forever—”
(23) Therefore Yahweh God sent him out from the garden of Eden, to till the ground from which he was taken.
Nevertheless, God did not competely abandon mankind. The verses I quoted showed that some experienced the presence of God at times. You were suggesting that all men, including Jesus, have been seperated from God, but God has worked though many people and was certainly working through Jesus, and God was with him (Acts 10:38).