How does a person who is dead in trespasses and sins get brought out of that deadness?

Every human being is dead in trespasses and sins until God brings them out of that deadness. This deliverance comes by an act of God when a person believes the Gospel, according to the biblical teaching. It is God's action, not something the individual produces.

Les explains that because Christ died for all, every last human being was dead in trespasses and sins. That deadness ends only when God performs an act to bring them out of it, and this occurs when we believe the Gospel. Paul's 'wherefore' in 2 Corinthians 5:16 points back to this accomplished work of Christ's death, burial, and resurrection, not to John the Baptist or Bethlehem.

2 Corinthians 5:14

For the love of Christ constraineth us; because we thus judge, that if one died for all, then were all dead:

2 Corinthians 5:16

Wherefore henceforth know we no man after the flesh: yea, though we have known Christ after the flesh, yet now henceforth know we him no more.

Were all people dead in trespasses and sins until God brought them out of it when they believed the gospel?

Yes. The context teaches that because Christ died for all, every last human being was dead in trespasses and sins until God brought them out of that deadness by an act of God when they believed the Gospel. This applies to all people, not merely some.