If God is everywhere present everywhere in the universe, then in what sense will unbelievers be separated from Him? The Bible says of unbelievers.

They will be punished with everlasting destruction and shut out from the presence of the Lord and from the majesty of his power (2Th 1:9)

How can someone be out of God's presence if God is everywhere? Is this not a contradiction?

God Is Present in His Wrath

The answer is found in the description of the wicked in the Book of Revelation.

He, too, will drink of the wine of God's fury, which has been poured full strength into the cup of his wrath. He will be tormented with burning sulfur in the presence of the holy angels and of the Lamb (Rev 14:10).

God will be present in judgment in the sense of His wrath. His immediate presence is what is missing in judgment. There is no relationship with God for those who are condemned.

Summary

One of the central truths of Scripture is the omnipresence of God—He is everywhere present in the universe and nothing can escape His notice. This is not contradicted by the idea of people being banished from His presence. This speaks of God's judgment. God is present with unbelievers in the sense of His wrath—His judgment is upon them. However His immediate presence is not with them. This is because they have no relationship with Him.