This question is based off of an assumption that the spiritually dead could not go to “Paradise.” This, however, overlooks the fact that sins were not taken away until the atonement was completed (Hebrews 10:1-4). While the OT saints had life, they only had it in view of the cross of Christ. Under the Law they were still considered spiritually dead.
So, everyone under the Law died in a state of spiritual separation because of man’s inability to follow the law perfectly. The difference lies within if they tried to keep the law or not. One group was destined to rise to eternal life, but the other was destined to shame and everlasting contempt (Daniel 12:2) Therefore, Christ could give His soul as an offering and still go to “Paradise” because of His perfect keeping of the Law.