Scripture makes it clear that God is present everywhere:

Am I a God near at hand, says the LORD, And not a God afar off? (Jer 23:23)

If God is everywhere present, then how could Adam and Eve be banished from His presence?

Visible Presence Limited

Though God is not limited to any one place, sometimes His visible presence is localized. For example, God speaks of Himself as being manifest in the Ark of the Covenant (Exd 25), the burning bush (Exd 3), and the pillar of fire (Exd 13:21), as well as many other places in Scripture. It is in that localized sense that Adam and Eve could be sent away from God's presence. Humanity cannot go to some place where God has no knowledge of them—we cannot hide from God.