The Old Testament saints could not go to heaven before Christ literally came to make atonement for sin and defeat death. That's why the Old Covenant faithful saints were in the bosom of Abraham. They did not go to the same place of the dead as the rich man, who was merely dead and buried. They, like poor Lazarus were carried by the angels of God to the bosom of Abraham to wait for the promised Messiah to come and set the captives free.
The building Paul says we have from the moment we have been born again is not of this earth but is a city whose builder and maker is God, that is a heavenly home for He has prepared for us a city. Through Christ's Spirit in us, we have gone spiritually, not bodily into the city of the living God, the heavenly Jerusalem, and an innumerable company of angels, to the general assembly and church of Christ (firstborn) as spirits of just men made perfect.
Hebrews 12:22-24 (KJV) But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect, And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
Hebrews 11:8-10 (KJV) By faith Abraham, when he was called to go out into a place which he should after receive for an inheritance, obeyed; and he went out, not knowing whither he went. By faith he sojourned in the land of promise, as in a strange country, dwelling in tabernacles with Isaac and Jacob, the heirs with him of the same promise: For he looked for a city which hath foundations, whose builder and maker is God.
Hebrews 11:16 (KJV) But now they desire a better country, that is, an heavenly: wherefore God is not ashamed to be called their God: for he hath prepared for them a city.
When Christ died on the cross, after His resurrection the graves of these faithful saints were opened and as spiritual bodies came out of the grave and went with Christ into heaven, now after the cross when we die those who have been born again through the Spirit of Christ within ascend to heaven to be with Christ a spiritual body/living soul to wait there until this time for building the Kingdom of God in heaven is complete.
Matthew 27:52-53 (KJV) And the graves were opened; and many bodies of the saints which slept arose, And came out of the graves after his resurrection, and went into the holy city, and appeared unto many.
Ephesians 4:8-10 (KJV) Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men. (Now that he ascended, what is it but that he also descended first into the lower parts of the earth? He that descended is the same also that ascended up far above all heavens, that he might fill all things.)
In death we don't lose what we already possess, that is eternal life through spirit in the spiritual Kingdom of God in heaven, kept alive by the Spirit of Christ within us. That's why Paul writes that not even death shall separate us from the love of God that is in Christ Jesus our Lord. (Ro 8:35-39)