Paul gives commentary as to what "Dead" means and looks like, if we keep reading..."...even when we were dead in trespasses, made us alive together with Christ (by grace have you been saved)" (Eph. 2:5). Here Paul locates the time when regeneration occurs. It takes place 'when we were dead.' With one thunderbolt of apostolic revelation all attempts to give the initiative in regeneration to man are smashed. Again, dead men do not cooperate with grace. Unless regeneration takes place first, there is no possibility of faith.
This says nothing different from what Jesus said to Nicodemus. Unless a man is born again first, he cannot possibly see or enter the kingdom of God. If we believe that faith precedes regeneration, then we set our thinking and therefore ourselves in direct opposition not only to giants of Christian history but also to the teaching of Paul and of our Lord Himself. Sproul.
Eph 2:2-3 ESV in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience— among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind.
This passage says nothing of whether or not we can respond to God. Saying "dead men do not cooperate with grace" is saying something that the texts does not speak on itself, right wrong or indifferent.