Paradise is what we call heaven. The Bible makes no distinction that Paradise is a different place than heaven.
When Jesus was crucified along with two thieves, one of the thieves repented and asked Jesus to remember him.
"And he was saying, 'Jesus, remember me when You come in Your kingdom!' And He said to him, 'Truly I say to you, today you shall be with Me in Paradise.'" (Luke 23:42-43)
So heaven and Jesus' kingdom and Paradise are synonymous. This is where God's throne is.
After Jesus died on the cross, He went directly to God the Father who is in heaven. Jesus said on the cross before He died: "'Father, into Your hands I commit My spirit.' Having said this, He breathed His last." (Luke 23:46)
So Jesus (His spirit) went directly to heaven (which is Paradise). The thief who repented also went directly to heaven. Jesus resurrected bodily three days later.
Elsewhere in the book of Revelation, Jesus tells us that one of the rewards in heaven is to eat from the tree of life:
"He who has an ear, let him hear what the Spirit says to the churches. To him who overcomes, I will grant to eat of the tree of life which is in the Paradise of God." (Revelation 2:7)
So the tree of life is in heaven (Paradise).
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Going to heaven through Jesus is by faith. Faith is like a credit system. Believers who lived during Old Testament times trusted that God would save them somehow. They had faith like a credit card. So they could go to heaven on credit. And Jesus paid for it afterwards.
We can see this in the book of Habakkuk in the Old Testament, where it says that those considered righteous by God are not proud of their deeds but live by faith.
"Behold, as for the proud one,
His soul is not right within him;
But the righteous will live by his faith." (Habakkuk 2:4)
So in the Old Testament, the concept of salvation by faith was already there. Because the gospel was not revealed fully, many of the Old Testament believers did not understand what the Messiah would do. That was ok in those times, because God didn't expect people to understand.
In fact, one of the earliest versions of the Old Testament gospel was simply that Abraham would have a descendant who would save the world.
The Bible says:
"Even so Abraham believed God, and it was reckoned to him as righteousness. Therefore, be sure that it is those who are of faith who are sons of Abraham. The Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, 'All the nations will be blessed in you.' So then those who are of faith are blessed with Abraham, the believer." (Galatians 3:6-9)
This means:
Abraham was credited with righteousness before the time of Christ. God deemed Abraham righteous, because he believed God's word as it was revealed to him.
God preached a shortened version of the gospel to Abraham: "All the nations will be blessed in you." (Galatians 3:8).
So Abraham did not have the full gospel at all. When Abraham died, he went to heaven on credit because he had faith in God. Later on, Jesus paid on the cross for Abraham and all the Old Testament saints retroactively.
We can see that the credit system was at work even before Jesus went to the cross.
Elijah and Moses appeared in glory before Jesus went to the cross to pay for their sins.
"And behold, two men were talking with Him; and they were Moses and Elijah, who, appearing in glory, were speaking of His departure which He was about to accomplish at Jerusalem. Now Peter and his companions had been overcome with sleep; but when they were fully awake, they saw His glory and the two men standing with Him." (Luke 9:30-32)
This wasn't a dream, because Peter and his companions saw Moses and Elijah in glory with Jesus when they were fully awake. How did Moses and Elijah appear in glory after they committed sins on earth?
In view of what Jesus would do on the cross, they got the goods (heaven and glory) beforehand, while Jesus paid for them afterwards.
So we see that faith is a credit system. Jesus paid for people's sins with His blood on the cross once and for all, whether they lived before His time or after.
Since the Old Testament saints were already in heaven when Jesus died on the cross, they could have witnessed what was going on on earth and understood as the events unfolded.
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Hebrews 12:1 says that Old Testament saints are witnesses surrounding us.
"Therefore, since we have so great a cloud of witnesses surrounding us, let us also lay aside every encumbrance and the sin which so easily entangles us, and let us run with endurance the race that is set before us, fixing our eyes on Jesus, the author and perfecter of faith, who for the joy set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God." (Hebrews 12:1)
Perikeimenon (περίκείμενον) is the Greek word used here, which means "lying around us" or "surrounding us." The phrase perikeimenon hēmin nephos ("a cloud lying around us") evokes an imagery of a stadium where spectators surround athletes. This phrase suggests that the saints in heaven are actively present and attentive to what's going on on earth, rather than being distant or inactive.
So as they saw what happened to Jesus (including His death, resurrection, His sitting down at the right hand of God the Father, and the gospel that the early Christians taught), they understood the gospel as they witnessed all these events from heaven.