Probably the best Biblical texts for this claim come from Paul’s writings to the Corinthian believers, particularly in 2 Corinthians. The letter can be divided into three sections:
1) 2 Corinthians 1-7 are arguments as to why Paul is not at Corinth in spite of the fact that he told them he would be back by that time. The section addressed the fact that “life change transformation” was part of the New Covenant process that will be consummated with Israel later (Isa. 59, Jer. 31, Rom. 11) but for the time being is foreshadowed by the change in them. As a result of their transformation, Paul had no fear for them, but wanted to answer some of their discomfort over Paul’s apparent neglect of his word.
2) 2 Corinthians 8-9 offer twenty principles of giving, as Paul attempted to get the church motivated and organized to complete an offering that was to be sent to the Jerusalem believers. Paul explained his expectation of the church as the time drew near to take the offering to Judea.
3) 2 Corinthians 10-13 offers another defense of Paul’s leadership, as Paul answers some unbelieving Judaizing critics that have attacked his leadership and Apostleship. Paul openly answers some of the criticism of the Judaizers that have been affecting the people’s thinking.
To answer the question I would zero in on two specific areas of 2 Corinthians. First, I would look closely at Paul’s argument in 2 Cor. 3-5 on the New Covenant life change. In the argument, Paul says that the New Covenant that God promised Israel and Judah has been foreshadowed in fulfillment by the changed lives of the people of Corinth that were being transformed inside by the Spirit. In that context he said that the Law brought a ministry of death and condemnation (in that sacrificial animals died because of it) and the new covenant brought the Spirit, glory and righteousness (3:1-13). He noted that Judaizers were experiencing the blinding of their hearts but that those who followed were an encouragement, causing Paul not to lose heart (13:14-14:18). Paul also said that any affliction now is less important than the glory he will get in the end, when his mortal body is “swallowed up in immortality” and he becomes “absent” from this body but “present to the Lord. (2 Cor. 5:1-9).
Here Paul plainly taught that when the body was dispensed with, his spirit would immediately be in the Lord’s presence. This is what Jesus taught as well. Consider that if we look closely at Paul’s description of “Paradise” as the “Third Heaven” of 2 Cor. 12:2-4 we see that the first heaven is the atmosphere of the earth, the second heaven is the starry canopy and the third is the place we call Paradise, or where God dwells. Paul makes clear that “Paradise” and “Heaven” (the abode of God are the same in 2 Cor. 12. Why is that important? Because we recall that Jesus said to the thief on the cross that “Today you shall be with me in Paradise” (Lk. 23:42,43). That would mean that on the very day of the thief’s death, he could be with Jesus in the third Heaven.
Both Jesus and Paul taught that to be absent from this physical body as a believer is to join in the presence of the Lord, in Paradise. The judgment that follows appears in the context of being with the Lord already (2 Cor. 5:10-11).