Why were the Gentiles without hope and without God in the world?

Gentiles were aliens from the commonwealth of Israel and strangers from the covenants of promise. God was dealing with covenant promises that belonged only to Israel, so Gentiles had no rights or access to them, leaving them without hope and without God in the world.

Les explains that Gentiles had no rights or access to Israel's government or commonwealth. Ephesians 2:12 calls them aliens from the commonwealth of Israel and strangers from the covenants of promise. Since the covenants belonged to Israel, Gentiles could not claim them; that condition was the law of the Gentiles, having no hope and without God in the world. God was dealing with covenant promises only for Israel until she became a prepared, spiritual, obedient people, and then He would send them into the Gentile world to bring Gentiles to a knowledge of their God. But Israel, having 2,000 years of being told they were special, could not accept that anybody else was worth anything.

Ephesians 2:12

That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:

What did Paul mean when he said the Gentiles had no hope and were without God?

Paul meant that while God was dealing with Israel on the Old Testament covenant basis, Gentiles were outside Israel's commonwealth and covenants of promise. They were without Christ, strangers to those promises, so they had no hope and were without God in the world.