That is your add and subtract from God's word.
Dead in trespasses is about not purifying yourself with the purification works of the law.
If a person doesn't first believe, then do you not get saved.
Again, how does a spiritually dead person believe if God does not make them alive with Christ?
I doubt you will actually read scripture and discern what God is saying, but I will try again anyway.
Ephesians 2:1-10
And you were dead in the trespasses and sins 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. But God, being rich in mercy, because of the great love with which he loved us, even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved— and raised us up with him and seated us with him in the heavenly places in Christ Jesus, so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus. For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.