Let’s first look at some things Jesus said:
"He said to another man, “Follow me.” But he replied, “Lord, first let me go and bury my father.” Jesus said to him, “Let the dead bury their own dead, but you go and proclaim the kingdom of God.” " (Luke 9:59-60, NIV)
(This implies that those who believe in Jesus and proclaim the Kingdom of God are not spiritually dead.)
“To the angel of the church in Sardis write: These are the words of him who holds the seven spirits of God and the seven stars. I know your deeds; you have a reputation of being alive, but you are dead. … Yet you have a few people in Sardis who have not soiled their clothes. … I will never blot out the name of that person from the book of life.” (Revelation 3:1,4-5)
So you can clearly be spiritually dead in Jesus’ eyes. In the end, that will lead to physical death. And being spiritually alive will lead to eternal physical life.
Now on to Paul:
“We are those who have died to sin; how can we live in it any longer? Or don’t you know that all of us who were baptized into Christ Jesus were baptized into his death? We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life. … In the same way, count yourselves dead to sin but alive to God in Christ Jesus. … offer yourselves to God as those who have been brought from death to life …
“When you were slaves to sin, you were free from the control of righteousness. What benefit did you reap at that time from the things you are now ashamed of? Those things result in death! But now that you have been set free from sin and have become slaves of God, the benefit you reap leads to holiness, and the result is eternal life. For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.”
(Romans 6:2-4,11,13,20-23, NIV)
Through Jesus, God has made us spiritually alive. Which will lead to eternal physical life. But if we renounce this gift, we will reap death.
The New Testament has an “already-but-not-yet” theology. The Kingdom of God is already here, but it will fully arrive when Jesus returns. The same applies to life and death. We are already spiritually alive. And when Jesus returns we will gain eternal physical life. (1 Thessalonians 4:13-18)